“n choose k”: \[{n \choose k}=\frac{n!}{k!(n-k)!}\]
Binomial theorem: \[(a+b)^n=\sum_{k=0}^n{{n \choose k}a^{n-k}b^k}\]
Pascal’s identity: \[{n \choose k}+{n \choose k-1}={n+1 \choose k}\]