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Two persons A and B have equal number of sons. There are three cinema tickets which are to be distributed among sons of A and B . The probability that all the tickets go to sons of A is 1 20 . The number of sons to each of them is

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

A. 3

Step-by-step solution

Let A , B have n sons each Total cases = 2 n C 3 Favourable cases = n C 3 Probability = n C 3 2 n C 3 = 1 20 ⇒ n n - 1 n - 2 2 n 2 n - 1 2 n - 2 = 1 20 ⇒ 10 n 2 - 3 n + 2 = 4 n 2 - 6 n + 2 ⇒ 10 n 2 - 30 n + 20 = 4 n 2 - 6 n + 2 ⇒ 6 n 2 - 24 n + 18 = 0 ⇒ 6 n 2 - 4 n + 3 = 0 ⇒ n = 1, 3 n = 1 i s r e j e c t e d

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