Question 1154722
<i>In how many ways can a dance committee of 15 students be chosen?</i>
<pr>
36C15 = {{{36!/(15!*21!)}}} = 5,567,902,560
<pr>
<i>In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 6 sophomores, 4 juniors, and 3 seniors?</i>
<pr>
9C2 * 9C6 * 10C4 * 8C3 = {{{(9!/(2!*7!))*(9!/(6!*3!))*(10!/(4!*6!))*(8!/(3!*5!))}}} = 36 * 84 * 210 * 56 = 35,562,240