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31 July, 12:53

A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a) If a study group is to consist of 2 freshmen, 3 sophomores, and 1 junior, how many different ways can the study group be selected? b) If a study group consisting of 6 students is selected, what is the probability that the group will consist of 2 freshmen, 3 sophomores, and 1 junior?

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  1. 31 July, 13:16
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    175/1001

    Step-by-step explanation:

    (a.)

    Freshman: 5 Combination 2

    sophomores: 7 Combination 3

    Junior: 4 Combination 1

    The combination of three groups:

    =5c2 * 7c3 * 4c1

    =10 * 35 * 4

    =1400 ways

    (b.)

    =5+7+4=16

    =2+3+1

    Which is (16 combination 6)

    The probability will be:

    = (5c2 * 7c3 * 4c1) / 16c6

    =1400/8008

    =175/1001
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