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6.Permutation and Combination
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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, $\frac{y}{9 x}=$
A
$5$
B
$4$
C
$8$
D
$9$
(IIT-2017)
Solution
$\mathrm{x}=10!$
$\mathrm{y}={ }^{10} \mathrm{C}_1 \times{ }^9 \mathrm{C}_8 \times \frac{10!}{2!}$
$\Rightarrow \frac{\mathrm{y}}{9 \mathrm{x}}=\frac{{ }^{10} \mathrm{C}_1 \times{ }^9 \mathrm{C}_8}{9 \times 2!}=\frac{10 \times 9}{9 \times 2}=5$
$\Rightarrow 5$
Standard 11
Mathematics
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