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List the coefficients in the row of Pascal's triangle corresponding to n = 7.

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9514 1404 393

Answer:

1 7 21 35 35 21 7 1

Explanation:

Numbering from k=0 to k=7, the k-th coefficient in the row is ...

C(7, k) = 7!/(k!(7-k)!)

You know the first two in row 7 are 1 and 7. There are 8 in the row, and the row is the same forward and backward. This means you only need to find C(7, 2) and C(7, 3). These are ...

C(7, 2) = 7!/(2!(5!)) = 7·6/(2·1) = 21

C(7, 3) = 7!/(3!(4!)) = 7·6·5/(3·2·1) = 35

So, row 7 is ...

1, 7, 21, 35, 35, 21, 7, 1

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