Question

12) There are 10 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are

possible?
A) 24
B) 5040
C) 210
D) 10,000

Answer 1

To determine the number of different subcommittees of 4 members from a board of 10, we use the combinations formula. The correct calculation is C(10, 4), resulting in 210 different subcommittees.

Step-by-step explanation:

To find out how many different subcommittees of 4 members can be formed from a board of 10 members, we need to calculate the number of combinations possible, which is done using the binomial coefficient. This often represented as 10 choose 4 or C(10, 4).

The formula for combinations is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items, k is the number of items to choose, and ! denotes factorial. Using this formula for our case: C(10, 4) = 10! / (4! * (10-4)!).

Calculating this we get:

1. 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
2. 4! = 4 * 3 * 2 * 1
3. (10-4)! = 6! = 6 * 5 * 4 * 3 * 2 * 1
4. C(10, 4) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
5. C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

The number of different subcommittees possible is 210.