There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?

That would simply be "choose 3 from 8" or

C(8,3) = 56

To determine the number of different subcommittees that can be formed, we need to use the concept of combinations.

In this case, we want to find the number of ways to choose 3 members out of a total of 8 members. This can be calculated using the formula for combinations, which is denoted as "nCr" or "C(n, r)".

The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

Where:
n! denotes the factorial of n, which is the product of all positive integers from 1 to n.
r! denotes the factorial of r.
(n-r)! denotes the factorial of (n-r).

Applying this formula to our problem, we have:

C(8, 3) = 8! / (3!(8-3)!).

Simplifying the expression:

C(8, 3) = 8! / (3!5!).

Using the factorial definition:

C(8, 3) = 8 * 7 * 6 / (3 * 2 * 1).

Evaluating the expression:

C(8, 3) = 56.

Therefore, there are 56 different subcommittees that can be formed from a board of 8 members.