Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let be the number of such words where no letter is repeated; and let be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Th

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, $\frac{y}{9 x} =$ [2017]

Smart Achievers · Accepted Answer

(5)

$x = 10! and y = {}^{10}C_{1} \times {}^{9}C_{8} \times \frac{10!}{2!} = 10 \times 9 \times \frac{10!}{2!}$

$∴$ $\frac{y}{9 x} = \frac{10 \times 9 \times \frac{10!}{2}}{9 \times 10!} = 5$

Solution

Q.
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]

Ans.
(5)

$x = 10! and y = {}^{10}C_{1} \times {}^{9}C_{8} \times \frac{10!}{2!} = 10 \times 9 \times \frac{10!}{2!}$

$∴$ $\frac{y}{9 x} = \frac{10 \times 9 \times \frac{10!}{2}}{9 \times 10!} = 5$

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Solution

Q. 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, y9x= [2017]

Ans. (5) x=10! and y=C110×C89×10!2!=10×9×10!2! ∴ y9x=10×9×10!29×10!=5

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Q.
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]

Ans.
(5)

$x = 10! and y = {}^{10}C_{1} \times {}^{9}C_{8} \times \frac{10!}{2!} = 10 \times 9 \times \frac{10!}{2!}$

$∴$ $\frac{y}{9 x} = \frac{10 \times 9 \times \frac{10!}{2}}{9 \times 10!} = 5$