Explore topic-wise MCQs in Permutations & Combinations.

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Number of circular permutations of different things taken all at a time is n!.

There are 20 points in a plane, how many triangles can be formed by these points if 5 are colinear?

Find the number of rectangles and squares in an 8 by 8 chess board respectively.

Find the sum of all four digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without repetition.

Find the number of ways of arranging the letters of the words DANGER, so that no vowel occupies odd place.

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

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?

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 colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them?

In a society, it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 hand shakers. Which one among the following numbers indicates the possible number of hugs?

In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?

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

How many 3-letter words can be formed out of the letters of the word CORPORATION , if repetition of letters is not allowed?

In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?

A person can go from place P to Q by 7 different modes of transport, but is allowed to return back to P by any mode other than the one used earlier. In how many different ways can he complete the entire journey?

How many words can be formed by using all letters of word ALIVE.

A briefcase has a number-lock system containing a combination of 3 digits (Each digit can be of numbers 0 to 8). If the correct combination is unknown, how much maximum time would be required to open the bag if each trial of combination takes 3 seconds?

On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?

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?

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?

The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is -.

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?

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

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?

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

Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving

I. Single flag of different colours

II. Any two flags in a different sequence of colours.

III. three flags in a different sequence of colours.

The maximum number of codes that can be generated 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?

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?

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

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

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

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

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}

There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?

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

In a class, there are 15 students. During a Christmas party all of them shook hands with each other only once. How many handshakes took place in the class?

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

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

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?

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

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

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

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 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?

Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?

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?