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
B
30240
C
99748
D
42386

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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