Vandermonde’s identity (convolution of binomials) (C(m+n,r) equals sum over k of C(m,k)C(n,r−k): choose k from first group)
jee-mainjee-advanced
C(m+n,r) equals sum over k of C(m,k)C(n,r−k) — choose k from first group and r−k from second
What each symbol means
| Symbol | What it stands for |
|---|---|
| k | Split between pools |
| m | Size of first pool |
| n | Size of second pool |
| r | Total items to choose |
When to use this
Non-negative integers; define C(a,b)=0 if b<0 or b>a so the sum naturally truncates.