Number of words

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Number of words

by rahul goyal » Thu Aug 12, 2010 1:53 am
Eight different letters of an alphabet are given.
Words of four letters from these are formed.
The number of such words with atleast one letter repeated is:

(a) \binom{8}{4}-^8P_4
(b) 8^4+\binom{8}{4}
(c) 8^4-^8P_4
(d) 8^4-\binom{8}{4}
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by kmittal82 » Thu Aug 12, 2010 2:30 am
Sorry, I dont understand the answer options you have posted.

Maximum ways to form words (i.e. when all letters can be repeated) = 8^4

Number of ways to form words where no letter is repeated = 8 x 7 x 6 x 5

Total number of ways in which atleast 1 letter is repeated = 8^4 - (8x7x6x5)