Easy Practice — Set 2

Quick Recap — Combinations

• Combinations (order irrelevant): $^nC_r=\dfrac{n!}{r!(n-r)!}$.
• $^nC_0=^nC_n=1$, $^nC_1=n$, and the symmetry $^nC_r=^nC_{n-r}$.
• Pascal: $^nC_r+^nC_{r-1}=^{n+1}C_r$; the row sum $\sum_r{}^nC_r=2^n$.
• Choosing a subset uses combinations; arranging it uses permutations.