Question

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

A
105
B
10P5
C
10510P5
D
510

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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