compute (40)+(51)+(62)+(73).
In general: (mn)=m!n!(m−n)!
so:
(40)=1(51)=5(62)=15(73)=35
I’ll leave you to add up the numbers!
(Note that 0! = 1)
Note that
C(n, 0) + C(n+1,1) + C(n + 2, 2) + C(n + 3, 3) +.....+ C(n + m, m) = C(n + m + 1, m)
So
C(4,0) + C(5, 1) + C(6,2) + C(7,3) = C(8,3) = 56