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JEE Advanced Mathematics question

MathematicsPermutations and CombinationsJEE Advanced

A word has 4 identical letters and some different letters. If the total number of words that can be made with the letters of the word be 210 then the number of different letters in the word is

Answer: (C)

Solution

Let there be letters other than the 4 identical ones, all distinct. The number of arrangements is

= 210 ⇒ (n+4)(n+3)·s 5 = 210 = 7·6·5 ⇒ n + 4 = 7 ⇒ n = 3.

So the word has 3 letters occurring once plus the

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Question ID VK-110417