A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 f

Discussion in 'Calculator Requests' started by math_celebrity, Apr 8, 2019.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    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.

    • Freshmen choices: 6 C 2 = 15
    • Sophomore choices: 9 C 3 = 84
    • Junior choices: 7 C 4 = 35
    • Senior choices: 7 C 5 = 21
    The number of committees we can choose is the product of combinations of 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
     

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