8 professors and 11 students are available to serve on committee. (a) How many ways can a committee of four people be selected? (b) How many

Question

8 professors and 11 students are available to serve on committee. (a) How many ways can a committee of four people be selected? (b) How many committees can be formed if each committee must have 3 professors and 4 students?

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Aaliyah 5 days 2021-11-22T10:06:27+00:00 1 Answer 0 views 0

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    2021-11-22T10:08:15+00:00

    Answer: a) 3876   b) 18480

    Step-by-step explanation:

    Given , The number of professors = 8

    The number of students are available = 11

    Total persons = 8+11=19

    a) The number of ways to select 4 people = ^{19}C_{4}

    =\dfrac{19!}{4!(19-4)!}\ \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\=\dfrac{19\times18\times17\times16\times15!}{24\times15!}\\=3876

    Hence, the number of ways to select 4 people  = 3876.

    b) Number of ways to choose 3 professors and 4 students = ^{8}C_{3}\times^{11}C_{4}

    =\dfrac{8!}{3!(8-3)!}\times\dfrac{11!}{4!(11-4)!}\\\\=56\times330\\\\=18480

    Hence, the numbers of ways to form a committee with 3 professors and 4 students = 18480.

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