JEE Advanced 2017 · Paper 1 · Mathematics Q11

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MathematicsInteger+3Question 47 of 54

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, $\frac{y}{9x} =$

Your answer

Answer and worked solution

Official answer: 5

No repeats. $x=10!$ .

Exactly one letter twice. Choose the doubled letter (10 ways) and the 8 other distinct letters from the remaining 9 ( $\binom98=9$ ways). Then arrange: $\dfrac{10!}{2!}$ ways.
$y=10\cdot9\cdot\frac{10!}2=45\cdot10!.$

Ratio.
$\frac y{9x}=\frac{45}9=5.$

Answer: 5

Topics:Permutations

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JEE Advanced 2017 · Paper 1, Mathematics question 11