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Question

Ten different letters of alphabet are given, words with five letters are formed with these given letters. Then the number of words which have at least one letter repeated


A
69760
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B
30240
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C
99748
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D
42386
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Solution

The correct option is B $$69760$$
$$10$$ letters $$5$$ to be selected 
Total number of $$5$$ letter words $$={ 10 }^{ 5 }$$
Number of words without repetition $$={}^{ 10 }{ P }_{ 5 }$$
Number of words without at least one letter repeated 
$$=100000-(10\times 9\times 8\times 7\times 6)\\ =69760 $$
Hence the correct answer is $$69760$$

Mathematics

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