Q64 / 120 · VITEEE 2017 · Mathematics

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

  • Correct answer
    A
    69760
  • B
    30240
  • C
    99784
  • D
    None of these

Solution

Total number of words that can be formed $=10^{5}$. Number of words in which no letter is repeated $={ }^{10} \mathrm{P}_{5}$. So, number of words in which at least one letter is repeated $=10^{5}-$ ${ }^{10} \mathrm{P}_{5}=69760$

Hence, the correct answer is option: 'A'.

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