Question

A word of $6$ letters is formed from a set of $16$ different letters of English alphabet (with replacement). Find out the probability that exactly two letters are repeated.

Answer 1

First we choose 5 letters from 16 different letters i.e. $\left(5^{16}\right)$ and then we have to those 5 letters to be repeated.

$\left(5^{16}\right)$ x5 and all the letters can be arranged in 6!. As two letters are repeated so the solution must be divided by 2!.

Hence the answer is :

$\frac{\left(5^{16}\right)\times 5\times 6!}{2!.{16}^6}$