Question 6 of 29
There are 8 seniors on the high school soccer team. Two of them will be chosen to be co-captains. How many ways are there to choose the cocaptains?
Decide if this is a permutation or a combination, and then find the number of ways to choose the co-captains.
A. Permutation; number of ways $= 56$
B. Combination; number of ways $= 28$
C. Permutation; number of ways $= 28$
D. Combination; number of ways $= 56$

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Answer

$28$

Steps

Step 1 ：This is a combination problem because the order of the co-captains does not matter. We need to find the number of ways to choose 2 co-captains from 8 seniors.

Step 2 ：Using the combination formula: $C (n, k) = \frac{n!}{k! (n - k)!}$ , where n = 8 and k = 2, we get $C (8, 2) = \frac{8!}{2! (8 - 2)!} = \frac{8!}{2! 6!}$

Step 3 ：Calculating the factorials: $8! = 8 \times 7 \times 6!$ and $2! = 2$

Step 4 ：Substituting the factorials into the combination formula: $C (8, 2) = \frac{8 \times 7 \times 6!}{2 \times 6!}$

Step 5 ：Simplifying the expression: $C (8, 2) = \frac{8 \times 7}{2} = 4 \times 7 = 28$

Step 6 ： $28$

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