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Question

Ten different letters of an alphabets are given. Words with five letters are formed from these given letters. The number of words, which have at least one letter repeated is


A
59720
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B
79260
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C
69760
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D
None of these
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Solution

The correct option is C $$69760$$
Number of words when repetition is allowed is $$10\times 10\times 10\times 10\times 10 = 10^{5}$$.
Number of words when repetition is not allowed is
$$10\times 9\times 8\times 7\times 6 = 30240$$.
Hence, required number of words in which at least one letter is repeated is $$10000 - 30240 = 69760$$.
1569063_1746810_ans_ab0d0de8e085445895df40ed75553cb8.jpg

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