Multiple choice

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

  1. 69760

  2. 30240

  3. 99784

  4. none of these
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A Correct answer
Explanation

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

AI explanation

First, calculate the total number of five-letter words possible from ten different letters, allowing repetition, which is 10 to the power of 5, or 100000. Next, calculate the number of five-letter words with no repetition using the permutation formula 10P5, which equals 10 times 9 times 8 times 7 times 6, or 30240. The number of words having at least one letter repeated is the total possible words minus the words with no repetition. Subtracting the two values gives 100000 minus 30240, which equals 69760.

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