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16 April, 11:02

From a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is formed randomly. What is the probability that

(a) there are exactly two professors on the committee;

(b) all committee members are of the same rank

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  1. 16 April, 12:10
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    Answer: a) 0.23

    b) 0.00085

    Step-by-step explanation:

    6 professors

    6 associate professors,

    10 assistant professors,

    12 instructors

    Committee: 6 people

    Total of combinations possible:

    C₃₄,₆ = 34! = 1344904

    6! 28!

    (a) there are exactly two professors on the committee;

    C₆,₂ * C₂₈,₄ = 6! * 28! = 15*20475 = 307125

    2! 4! 4! 24!

    P = 307125/1344904 = 0.23

    (b) all committee members are of the same rank

    All prof: C₆,₆ = 1

    All assoc. prof: C₆,₆ = 1

    All assist prof: C₁₀,₆ = 210

    All instr: C₁₂,₆ = 924

    1+1+210+924 = 1136

    P = 1136/1344904 = 0.00085
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