Question

select the correct answer.
a student club has 15 members. how many ways can a committee of 6 members be chosen?
a. 504
b. 720
c. 5,005
d. 3,603,600

Explanation:

Step1: Identify combination formula

We use combinations since the order of committee members does not matter. The formula for combinations is:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=15$ (total members) and $k=6$ (members to choose).

Step2: Substitute values into formula

$$C(15,6)=\frac{15!}{6!(15-6)!}=\frac{15!}{6! \times 9!}$$

Step3: Simplify the factorials

Cancel out $9!$ from numerator and denominator:
$$C(15,6)=\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$$

Step4: Calculate the result

$$\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10}{720}=5005$$

Answer:

C. 5,005