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In how many ways can 8 letters be chosen from a set of 24 letters, where 8 letters are identical as a, 8 letters are identical as b, and the remaining letters are all distinct?

1. 27
2. 8.2⁸
3. 10.2⁷
4. None of these

Correct answer: 10.2⁷

Solution

Letters: 8 a's, 8 b's, 8 distinct. Choose i a's and j b's (each 0..8) and fill the rest 8-i-j from the 8 distinct letters: total = sum over i,j of C(8, 8-i-j). Evaluating gives 1280 = 10*2^7.

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