43 + Mcqs in Permutations & Combinations in Mathematics Quizzes Page 1 McqOptions

1.	What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
A.	100
B.	60
C.	30
D.	20
Answer» D. 20

Discussion

2.	Using all the letters of the word “THURSDAY”, how many different words can be formed?
A.	8
B.	8!
C.	7!
D.	7
Answer» C. 7!

Discussion

3.	Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A?
A.	3
B.	6
C.	24
D.	120
Answer» C. 24

Discussion

4.	Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?
A.	One
B.	Zero
C.	Three
D.	Cannot be determined
Answer» E.

Discussion

5.	Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving_x005F_x000D_I. Single flag of different colours_x005F_x000D_II. Any two flags in a different sequence of colours._x005F_x000D_III. three flags in a different sequence of colours._x005F_x000D_The maximum number of codes that can be generated is.
A.	6
B.	9
C.	15
D.	18
Answer» D. 18

Discussion

6.	Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
A.	36
B.	81
C.	91
D.	116
Answer» D. 116

Discussion

7.	There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?
A.	15
B.	18
C.	24
D.	30
Answer» D. 30

Discussion

8.	The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?
A.	(6!)2
B.	6! * ⁷P₆
C.	2(6!)
D.	6! * 7
Answer» C. 2(6!)

Discussion

9.	The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
A.	4000
B.	2160
C.	4320
D.	5300
Answer» D. 5300

Discussion

10.	The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________?
A.	24
B.	23
C.	119
D.	120
Answer» D. 120

Discussion

11.	The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
A.	720
B.	144
C.	120
D.	36
Answer» C. 120

Discussion

12.	In how many ways can three consonants and two vowels be selected from the letters of the word “TRIANGLE”?
A.	25
B.	13
C.	40
D.	30
Answer» E.

Discussion

13.	In how many ways can live boys and three girls sit in a row such that all boys sit together?
A.	4800
B.	5760
C.	2880
D.	15000
Answer» D. 15000

Discussion

14.	In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?
A.	120
B.	720
C.	4320
D.	2160
Answer» C. 4320

Discussion

15.	In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?
A.	10080
B.	4989600
C.	120960
D.	None of these
Answer» D. None of these

Discussion

16.	In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
A.	120
B.	240
C.	360
D.	480
Answer» E.

Discussion

17.	In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?
A.	9
B.	12
C.	14
D.	18
Answer» C. 14

Discussion

18.	In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
A.	19
B.	120
C.	624
D.	1024
Answer» D. 1024

Discussion

19.	In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
A.	400
B.	500
C.	600
D.	20
Answer» C. 600

Discussion

20.	How many three letter words are formed using the letters of the word TIME?
A.	12
B.	20
C.	16
D.	24
Answer» E.

Discussion

21.	How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
A.	360
B.	60
C.	300
D.	180
Answer» B. 60

Discussion

22.	How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
A.	60
B.	360
C.	120
D.	240
Answer» B. 360

Discussion

23.	How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?
A.	40
B.	400
C.	5040
D.	2520
Answer» D. 2520

Discussion

24.	Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
A.	5
B.	6
C.	7
D.	8
Answer» D. 8

Discussion

25.	Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?
A.	720
B.	1440
C.	1860
D.	2160
Answer» C. 1860

Discussion

26.	A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?
A.	11
B.	30
C.	14
D.	20
Answer» D. 20

Discussion

27.	A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?
A.	5
B.	6
C.	7
D.	18
Answer» D. 18

Discussion

28.	A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________?
A.	4
B.	12
C.	18
D.	None of these
Answer» E.

Discussion

29.	A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?
A.	20
B.	40
C.	512
D.	1024
Answer» E.

Discussion

30.	A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
A.	63
B.	511
C.	1023
D.	15
Answer» D. 15

Discussion

31.	A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?
A.	10
B.	15
C.	20
D.	25
Answer» E.

Discussion

32.	A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
A.	12
B.	48
C.	36
D.	42
Answer» E.

Discussion

33.	A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________?
A.	216
B.	243
C.	215
D.	729
Answer» D. 729

Discussion

34.	A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A.	¹²C₅ * 10
B.	¹²C₇ * 10
C.	¹²C₇ * ¹⁰C₅
D.	12 * ¹⁰C₅
Answer» D. 12 * ¹⁰C₅

Discussion

35.	A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
A.	²²C₁₀
B.	²²C₁₀ + 1
C.	²²C₉ + ¹⁰C₁
D.	²²C₁₀ – 1
Answer» E.

Discussion

36.	A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
A.	300
B.	450
C.	600
D.	750
Answer» D. 750

Discussion

37.	A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
A.	300
B.	600
C.	750
D.	900
Answer» C. 750

Discussion

38.	A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A.	20
B.	54
C.	42
D.	60
Answer» B. 54

Discussion

39.	A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
A.	165
B.	185
C.	205
D.	225
Answer» B. 185

Discussion

40.	A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
A.	150
B.	200
C.	250
D.	300
Answer» C. 250

Discussion

41.	A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.	21
B.	12
C.	9
D.	108
Answer» E.

Discussion

42.	A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
A.	⁹C₂
B.	³C₂
C.	¹⁶C₂
D.	¹²C₂
Answer» D. ¹²C₂

Discussion

43.	2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
A.	15
B.	36
C.	48
D.	60
Answer» C. 48

Discussion

Explore topic-wise MCQs in Mathematics Quizzes.

What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?

Using all the letters of the word “THURSDAY”, how many different words can be formed?

Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A?

Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is________?

Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?

There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?

The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.

The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________?

The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?

In how many ways can three consonants and two vowels be selected from the letters of the word “TRIANGLE”?

In how many ways can live boys and three girls sit in a row such that all boys sit together?

In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together?

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?

How many three letter words are formed using the letters of the word TIME?

How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?

How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}

How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?

Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?

Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?

A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted?

A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?

A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?

A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?

A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________?

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?

A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?

A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?

A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?

A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?

A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?