Compute
\( \binom50+\binom51+\binom62+\binom71+\binom83+\binom92+\binom{10}4+\binom{11}3\)
.
nvm I got it. It's 23426. fourth number of the fifty third row of pascals triangle.
+128460
Using the identity : C(m, n) + C(m, n + 1) = C(m + 1, n + 1), we have
C(5,0) + C(5,1) + C(6,2) + C(7,1) + C(8,3) + C(9,2) + C(10,4) + C(11,3)
C(6,1) + C(6,2) + C(7,1) + C(8,3) + C(9,2) + C(10,4) + C(11,3)
C(7,2) + C(7,1) + C(8,3) + C(9,2) + C(10,4) + C(11,3)
C(7,1) + C(7,2) + C(8,3) + C(9,2) + C(10,4) + C(11,3)
C(8,2) + C(8,3) + C(9,2) + C(10,4) + C(11,3)
C(9,3) + C(9,2) + C(10,4) + C(11,3)
C(9,2) +C(9,3) + C(10,4) + C(11,3)
C(10,3) + C(10,4) + C(11,3)
C(11,4) + C(11,3)
C(11,3) + C(11,4)
C(12,4) =
495
