Multiple choice

Words of $4$ letters are to be formed from $10$ different letters. How many words are formed in which at least one letter is repeated?

  1. $10240$
  2. $2440$
  3. $6970$
  4. $4960$
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D Correct answer
Explanation

Total possible 4-letter words using 10 letters is 10^4 = 10000. Words with no repeated letters is 10 * 9 * 8 * 7 = 5040. The number of words with at least one repetition is 10000 - 5040 = 4960.

AI explanation

Using the fundamental principle of counting, the total number of 4-letter words that can be formed from 10 different letters where any letter can be used any number of times is 10 times 10 times 10 times 10, or 10000. The number of words with no repetition (all distinct letters) is calculated using the permutation formula 10P4, which is 10 times 9 times 8 times 7, equaling 5040. The number of words where at least one letter is repeated is the total minus the non-repeating words, so 10000 minus 5040 equals 4960.

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