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A word of 6 letters is formed from a set of 16 different letters of English alphabets (with replacement). Find the probability that exactly two letters are repeated.

A word of 6 letters is formed from a set of 16 different letters of English alphabets (with replacement). Find the probability that exactly two letters are repeated.

Grade:12th pass

1 Answers

Vasanth SR
askIITians Faculty 1335 Points
6 years ago
The first four letters, non-repeated, are chosen in a certain arrangement: A B C D = 16*15*14*13
There are 12 possibilities for the repeated letter 'E', and there are 6C2 ways to place the two 'E's into A B C D. (Look up balls and urns formula)
So you end up with 16*15*14*13*12*6C2 for the numerator.

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