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14 different letters of alphabet are given, words with 6 letters are formed from these given letters. How many number of words are there which have at least one letter repeated?

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14 different letters of alphabet are given, words with 6 letters are formed from these given letters. How many number of words are there which have at least one letter repeated?

(a) 892742

(b) 999988

(c) 213216

(d) 786730

I had been asked this question in semester exam.

My question is from Counting in section Counting of Discrete Mathematics

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Right answer is (b) 999988

Easy explanation: Number of words which have at least one letter replaced = total number of words – total number of words in which no letter is repeated, => 10^6 – ^12P6 => 1000000 − 924 = 999988.

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