Permutations and Combinations 3 Question 9
9. 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, $\frac{y}{9 x}=$
(2017 Adv.)
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Answer:
Correct Answer: 9. (5)
Solution:
- $x=10$ !
$y={ }^{10} C _1 \times{ }^{9} C _8 \times \frac{10 !}{2 !}=10 \times 9 \times \frac{10 !}{2} \Rightarrow \frac{y}{9 x}=\frac{10}{2}=5$
