Question

2n boys are divided into two sub-groups containing n boys each. The probability that the two tallest boys are in different groups is

(a) n/2n - 1

(b)  n - 1/2n - 1

(c)  2n - 1/4n²

(d)  None of these

Answer 1

Correct option (a) n/2n - 1

Explanation:

Total number of ways of dividing 2n boys in two equal groups is ²ⁿC_n . ⁿC_n . If we leave the two tallest boys, 2n–2 boys can be divided into two equal groups in ^2n–2C_n–1. 

^n–1C_n–1 ways and the two tallest boys can be arranged in different groups in 2! ways. 

The required probability is