Statistics

A committe of 5 members will be chosen from a group of 10 teachers and 5 students. What is the probability that the committee
will have
A) all teachers?
B) 3 teachers and 2 students?
C) 3 or 4 teachers?

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  1. Number of possible choices of 5 members from a total of 15
    = C(15,5) = 3003

    a) number of all teachers = C(10,5) = 252
    so prob(5 teachers) = 252/3003 = 12/143

    b) 3 teachers, and 2 students
    prob = C(10,3) * C(5,2)/3003 = ....

    c) not clear with the wording.
    Is it exactly 3 teachers or exactly 4 teachers, or is the case of 3 teachers included in 4 teachers?
    I will go with the "exactly".
    prob = ( C(10,3)C(5,2) + C(10,4)C(5,1) )/3003 =

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