Multiple choice

Ten different letters of alphabet are given, words with five letters are formed with these given letters. Then the number of words which have at least one letter repeated

  1. $69760$
  2. $30240$
  3. $99748$
  4. $42386$
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A Correct answer
Explanation

Total words of 5 letters using 10 letters is 10^5 = 100,000. Words with no letters repeated is 10 * 9 * 8 * 7 * 6 = 30,240. Words with at least one repetition = 100,000 - 30,240 = 69,760.

AI explanation

The total number of possible five-letter words using ten letters is 10^5, which equals 100000. The number of five-letter words with no repetition is given by the permutation 10P5, which calculates to 10 * 9 * 8 * 7 * 6 = 30240. Subtracting the non-repeated words from the total gives 100000 - 30240 = 69760.

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