To determine the number of ways a committee of 6 members can be chosen from a student club that has 15 members, we need to use the concept of combinations.
When selecting a committee, the order in which the members are chosen does not matter. This means we use the combination formula:
[tex]\[ C(n, k) = \frac{n!}{k! \cdot (n - k)!} \][/tex]
where [tex]\( n \)[/tex] is the total number of members and [tex]\( k \)[/tex] is the number of members to choose.
For this problem:
- [tex]\( n = 15 \)[/tex]
- [tex]\( k = 6 \)[/tex]
Substituting these values into the combination formula, we get:
[tex]\[ C(15, 6) = \frac{15!}{6! \cdot (15 - 6)!} \][/tex]
Simplifying the denominator:
[tex]\[ 15 - 6 = 9 \][/tex]
So the formula becomes:
[tex]\[ C(15, 6) = \frac{15!}{6! \cdot 9!} \][/tex]
After performing the calculations, we determine the number of ways to choose the committee is:
[tex]\[ C(15, 6) = 5,005 \][/tex]
Therefore, the number of ways a committee of 6 members can be chosen from 15 members is:
5,005
So the correct answer is:
OC. 5,005
