Question

algebra i b-cr
a coach chooses six out of eight players to go to a skills workshop.
if order does not matter, in how many ways can he choose the players for the workshop?
○ 6
○ 8
○ 28
○ 56

Explanation:

Step1: Identify combination formula

When order doesn't matter, we use the combination formula:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=8$ (total players), $k=6$ (players to choose)

Step2: Substitute values into formula

$$C(8,6)=\frac{8!}{6!(8-6)!}=\frac{8!}{6!2!}$$

Step3: Simplify the factorials

$$\frac{8\times7\times6!}{6!\times2\times1}=\frac{8\times7}{2\times1}$$

Step4: Calculate the final value

$$\frac{56}{2}=28$$

Answer:

28 (Option C)