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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

Respuesta :

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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