Permutations And Combinations Question 152

Question: 10 different letters of English alphabet are given. Out of these letters, words of 5 letters are formed. How many words are formed when at least one letter is repeated [UPSEAT 1999]

Options:

A) 99748

B) 98748

C) 96747

D) 97147

Show Answer

Answer:

Correct Answer: A

Solution:

  • Number of words of 5 letters in which letters have been repeated any times = $ 10^{5} $ But number of words on taking 5 different letters out of $ 10={{}^{10}}C_5=252 $ \ Required number of words = $ 10^{5}-252=99748 $ .

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