Combination Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
From a group of 66 men and 44 women, how many committees of 55 can be formed that include exactly 33 men and 22 women?

Solution

  1. 1
    Choose 33 men from 66: (63)=20\binom{6}{3} = 20.
  2. 2
    Choose 22 women from 44: (42)=6\binom{4}{2} = 6.
  3. 3
    By the multiplication principle, total committees =20×6=120= 20 \times 6 = 120.

Answer

120120
When a selection has multiple independent constraints, compute each sub-selection separately and multiply. This combines the combination formula with the counting principle.

About Combination

A combination is an unordered selection of objects — the number of ways to choose rr items from nn distinct items is C(n,r)=n!r!(n−r)!C(n,r) = \frac{n!}{r!(n-r)!}.

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More Combination Examples

Example 1 easy

A committee of [formula] is to be chosen from [formula] people. How many different committees are po

Example 3 medium

How many ways can you choose [formula] books from a shelf of [formula] books?

Example 4 medium

A pizza shop offers [formula] toppings. How many different [formula]-topping pizzas can be made if o

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