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We have four sets S1, S2, S3, S4 each containing a number of parallel lines. The set Si contains i + 1 parallel lines i = 1,2,3,4. A line in Si is not parallel to lines in Sj when i ≠ j. In how many points do these lines intersect ?
(A) 54
(B) 63
(C) 71
(D) 95
We have four sets S1, S2, S3, S4 each containing a number of parallel lines. The set Si contains i + 1 parallel lines i = 1,2,3,4. A line in Si is not parallel to lines in Sj when i ≠ j. In how many points do these lines intersect ?
(A) 54
(B) 63
(C) 71
(D) 95
Correct option: (C) 71
Explanation:
Number of point of intersection = 2C1 (3C1 + 4C1 + 5C1) + 3C1 (4C1 + 5C1) + 4C1 × 5C1
= 2(12) + 3(9) + 20
= 24 + 27 + 20
= 71