First slide

Permutations

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:

Easy

A

69760
B

30240
C

99748
D

None of these

Solution

Number of words in which all the 5 liters are repeated $= 10^{5}$ = 100000 and the number of words in which no letter is repeated = $P (10, 5) = 30240$
Hence the required number of ways $= 100000 - 30240 = 69760$

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