Multiple choice

Out of seven letters, a few of them are similar and others are different. If different words are formed taking all of them together, number of words formed is $210$, then the number of similar letters is

  1. 4

  2. 5

  3. 3

  4. 6
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A Correct answer
Explanation

Total letters = 7. Let n be the number of similar letters. The number of permutations is 7! / n! = 210. 5040 / n! = 210, so n! = 5040 / 210 = 24. Since 4! = 24, n = 4.

AI explanation

We test the options by dividing 7! by the factorial of the number of similar letters to match the 210 possible arrangements. Dividing 7! by 4! yields 5040 divided by 24, which equals 210. Since 7! divided by 3! yields 840 and 7! divided by 5! yields 42, only a group of 4 similar letters produces exactly 210 words.

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