Question

how many ways of selecting a 4 letter at a time from word examination

Answer 1

EXAMINATION has 11 letters, and in which 'A', 'I' and 'N', all occur twice. 11C4, would have been fine if all letters were distinct.

So, we have E, X, M, T, O, (AA), (II), (NN). 8 distinct letters.

1. 4 letters selected, which are all distinct: 8C4 = 70
2. 2 letters alike, and 2 distinct (eg: AAEX) = 3C1 x 7C2 = 63
3. 2 letters alike, and 2 letters alike (eg: AAII) = 3C2 = 3

So answer is, 70 + 63 + 3 = 136.

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