Chapter 10 - Section 10.2 - Permutations and Combinations - 10.2 Assess Your Understanding - Page 695: 28

$C(5,2)=10$

All the combinations of 5 objects a,b,c,d and e taken 2 at a time is $ab, ac,ad,ae,bc,bd,be,cd,ce,de$ Using the combination formula we obtain: $C(5,2)=\frac{5!}{(5-2)!2!}=\frac{5!}{3!2!}=\frac{5\cdot4\cdot3!}{3!\cdot2\cdot1}=10$ $C(5,2)=10$