Question

coach malone has 8 member volleyball team. he told his team that he would start six different players every game. how many games would it take tk dk this?

Answer 1

The problem is essentially asking, how many ways can you select 6 different players from a group of 8 players?

When order is important, we use the permutation formula and when order is not important, we use the combination formula.

Here, the order is not important , so we use the combination formula. Shown below:

`^nC_r=(n!)/((n-r)!r!)`

This is the number of ways to select r things from total n things.

We have

r = 6

n = 8

Substituting and simplifying, we have:

`\begin{gathered} ^nC_r=(n!)/((n-r)!r!) \\ ^8C_6=(8!)/((8-6)!6!) \\ =(8!)/(2!6!) \\ =(8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)/(2\cdot1\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1) \\ =(8\cdot7)/(2\cdot1) \\ =(56)/(2) \\ =28 \end{gathered}`

So,

Coach Malone would need 28 games to achieve his target.