Words of length 10 are formed using the letters $A, B, C$, $D, E, F, G, H, I, J$. Let $x$ be the num

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 such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$

Professor PC Thomas Classes · Answer

(5): We have $x=10$ ! Also, $y={ }^{10} C_{1} \cdot{ }^{9} C_{8} \cdot \frac{10!}{2!}=\frac{10 \cdot 9}{2} \cdot 10$ !\ Dividing we get, $\frac{y}{x}=\frac{10 \cdot 9}{2}=5 \cdot 9$\ $	herefore \frac{y}{9 x}=5$\