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Question

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is $$69760$$.


A
True
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B
False
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Solution

The correct option is A True
Number of words in which all the 5 letters are repeated $$= 10^5 = 100000$$.

and the number of words in which no letter is repeated

$$ ^{10}P_5 = 10 \times 9 \times 8 \times7 \times 6 = 30240$$.

Hence the number of words which have at least one letter repeated $$= 100000 - 30240 = 69760$$.

Maths

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