A committee will be selected from a group of 12 women and 18 men. The committee will consist of 5 women and 5 men. Which of the following expressions gives the number of different committees that could be selected from these 30 people?

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Since we are choosing groups, order does not really matter (it doesn't matter who is first in a group).

To select the women, we choose 5 members from 12:

$$ {}_{12}C_{5} $$

To select the men, we choose 5 members from 18:

$$ {}_{18}C_{5} $$

Each possible combination of women will be paired with each possible combination of men to get the total possible committees.

$$ ({}_{12}C_{5})({}_{18}C_{5}) $$