A bag contains `n` white and `n` red balls. Pairs of balls are drawn without replacement until the bag is empty. Show that the probability that each pair consists of one white and one red ball is `(2^n)/(^(2n)C_n)`

Explanation

Total no. of ways of selecting `n` pairs `=C_{n}^{2 n}`

No. of ways of selecting `n` pairs each with one white and one red

`=2 times 2 times 2 times 2 times 2 ldots . n` times

`=2^{{n}}`

`Rightarrow` Probability ` (2^n)/(\ ^(2n)C_n)`.