Permutation.
Probability
Level
2
Ten different letters of the 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
100000
10000
69760
30240
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1 solution
Number of 5 letters words (with the condition that a letter can be repeated) = 10x10x10x10x10 = 10^5
. The number of words using 5 different letters out of 10 is 10P5 . Therefore, the required number of letters = Total number of words – Total number of words in which no letter is repeated
= 10^5– 10P5 = 69760.