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

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

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