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?

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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?

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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:

[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]

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:

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

So,

Coach Malone would need 28 games to achieve his target.