find the terms and leave the coefficients as factorials:
Term with t^5 in (v-t)^17
That would be the sixth term.
For any positive integer n , the expansion of (x + y)n is C(n, 0)x n + C(n, 1)x n-1 y + C(n, 2)x n-2 y 2 + ... + C(n, n - 1)xy n-1 + C(n, n)y n .
Each term r in the expansion of (x + y)n is given by C(n, r - 1)x n-(r-1) y r-1 .