How many different three-member committees are there whose members are selected from a group of 10 people?

Answer: 120

Explanation: The problem can be solved using combination which is a mathematical approach used to determine the number of different possible arrangements from a certain collection where the order of arrangement isn't considered.

Combination is calculated using the formula:

nCr = (n!) : ((n-r) ! * r!)

In the question above;

n = 10, r = 3

Therefore,

nCr = 10C3

nCr = (10!) : ((10 - 3) ! * 3!)

nCr = 3628800 : (7! * 3!)

nCr = 3628800 : 5040 * 6

nCr = 3628800 : 30240

nCr = 120