Permutations And Combinations Question 21

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 [IIT 1980; MNR 1998, 99; DCE 2001]

Options:

A) 69760

B) 30240

C) 99748

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • 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 are $ ^{10}P_5=30240 $ . Hence the required number of ways are 100000 - 30240 = 69760.

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