Multiple choice

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

  1. $10^5$
  2. ${^1}{^0}P_5$
  3. $10^5-{^1}{^0}P_5$
  4. $5{^1}{^0}$
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C Correct answer
Explanation

Total words possible with 10 letters and 5 slots is 10^5. Words with no repeated letters are permutations 10P5. Words with at least one repetition = Total - Words with no repetition.

AI explanation

Using the complement principle, the total number of 5-letter words formed from 10 different letters allowing any letter to be used multiple times is 10^5. The number of words formed when all letters must be distinct is given by the permutation 10P5. Therefore, the number of words with at least one letter repeated is 10^5 - 10P5.

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