Question

a team of 8 players needs to select 2 captains. how many different pairs of captains can be chosen?
$_{8}c_{2} = ?$
hint:
$_{n}c_{r} = \frac{_{n}p_{r}}{r!}$

Explanation:

Step1: Recall combination formula

The combination formula is $C(n, r) = \frac{n!}{r!(n-r)!}$, where $n=8$ and $r=2$.

Step2: Calculate factorial values

$8! = 8×7×6!$, $2! = 2×1$, $(8-2)! = 6!$.

Step3: Substitute into formula

$C(8,2) = \frac{8×7×6!}{2×1×6!} = \frac{8×7}{2×1} = 28$.

Answer:

28