Question

Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9x}=$___

Answer 1

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