Question

What is C(8,5) in factorial notation?

Answer 1

The formula for the number of combinations of n objects taken r at a time is given by:

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

In this case, we have:

C(8, 5) = 8! / (5! * (8-5)!)

Simplifying the denominator:

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

Writing 5! and 3! in expanded form:

C(8, 5) = 8! / (5 * 4 * 3! * 3 * 2 * 1)

Cancelling out the 3! terms:

C(8, 5) = 8! / (5 * 4 * 3 * 2 * 1)

Writing 8! in expanded form:

C(8, 5) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1)

Cancelling out the 5 * 4 * 3 * 2 * 1 terms:

C(8, 5) = 8 * 7 * 6 / (3 * 2 * 1)

Simplifying:

C(8, 5) = 56

Therefore, C(8, 5) = 56 in factorial notation.