Mathematics - Permutation & Combination Question with Solution | TestHub

$x=$number of ways in which$10$ letter word can be formed using the given ten distinct letters.

$x=10!$

$y=$ number of ways, in which$10$ letter words can be formed, in which exactly $1$ letter is repeated twice and remaining $8$ letters are distinct.

$y={ }^{10}{C}_1\times { }^9{C}_8\times \frac{10!}{2!}$$=10\times 9\times \frac{10!}{2!}=5\times 9\times 10!$

$\frac{y}{9x}=\frac{5\times 9\times 10!}{9\times 10!}=5$