A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
We want combinations for freshmen, sophomores, juniors, and seniors.
Total Committees = Freshmen choices * Sophomore choices * Junior choices * Senior choices
Total Committees = 15 * 84 * 35 * 21
Total Committees = 926,100
We want combinations for freshmen, sophomores, juniors, and seniors.
- Freshmen choices: 6 C 2 = 15
- Sophomore choices: 9 C 3 = 84
- Junior choices: 7 C 4 = 35
- Senior choices: 7 C 5 = 21
Total Committees = Freshmen choices * Sophomore choices * Junior choices * Senior choices
Total Committees = 15 * 84 * 35 * 21
Total Committees = 926,100