Compute \( \binom40+\binom51+\binom62+\binom73.\)
I'm not sure how to solve these binomial expressions.
\(\dbinom{n}{k} = \dfrac{n!}{k!(n-k)!}\\ n! = n \cdot (n-1) \cdot (n-2) \cdot \dots \cdot 3 \cdot 2\)
Thanks!
Note that
C(n,m) + C(n + 1, m + 1) + C(n + 2, m + 2) + .....+ C( n + q, m + q) = C (n + q + 1, m + q)
So
C(4,0) + C(5, 1) + C(6,2) + C(7, 3) = C(8, 3) = 56
+43 
