excecutives from 25 student clubs, one male and one female from each are attending a workshop on student violence. how many ways can a commitee be set up of 5 men and 7 women if only one male or female from each club can be selected
2026-05-04 19:58:44.1777924724
excecutives from 25 student clubs, one male and one female...
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Use constructive counting. First select which $12$ of the $25$ clubs will have representatives. This can obviously be done in $\dbinom{25}{12}$ ways. Now that we have our subset, we must choose $5$ of these $12$ clubs to be represented by the male. This can be done in $\dbinom{12}{5}$ ways. Our final answer is $$\dbinom{25}{12} \times \dbinom{12}{5}$$ $$= \boxed{4,118,637,600}$$ possible committees.