9514 1404 393
Answer:
1 7 21 35 35 21 7 1
Step-by-step 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
