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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, y9x=   


Solution

Letters are A,B,C,D,E,F,G,H,I,J
Number of words that can be formed by 10 letters is =10!×10C10=10!
x=10!
Now for repetition one letter 
The perticular letter can be selected in 10C1 ways which is used twice in the word 
and now rest of the 8 letters can be selected from 9 letters can be done in 9C8
Hence number of word than can be formed =10C1×9C8×10!2!
y=10C1×9C8×10!2!y9x=10C1×9C8×10!2!9×10!=5

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