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Question

With 10 different letters, 5 letter words are formed. Then the number of words which have atleast one letter repeated is


A
105
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B
10P5
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C
10510P5
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D
510
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Solution

The correct option is C $$10^5-{^1}{^0}P_5$$
Total number of ways in which the 5 letter word can be formed with repetition allowed is $$10^5$$
The number of ways in which the 5 letter word can be formed where no digit is repeated is $$^{10}P_{5}$$
Thus the number of ways where at least one digit is repeated is 
$$10^5-^{10}P_{5}$$

Maths

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