In a community, 5 people from Koc group, 6 people from Sabanci group and 4 peopl

Question

In a community, 5 people from Koc group, 6 people from Sabanci group and 4 people from Independent group exist as representatives. One, who does not know all these representatives, creates a random committee with 3 people in total from these representatives. With respect to this, a) What is the probability of being represented in the committee with one person from each group? b) What is the probability of creating the committee from the representatives of the same group? c) What is the probability of creating the committee with 2 people from any of these three groups and 1 person from another group?

Explanation / Answer

(a)

P(one from each group) = (5C1*6C1*4C1)/(15C3) = 24/91 = 0.264

(b)

P(all from same group) = (5C3)/(15C3) + (6C3)/(15C3) + (4C3)/(15C3) = 34/455 = 0.0747

(c)

P( 2 from one group and 1 from any other) = (5C2*10C1)/(15C3) + (6C2*9C1)/(15C3) + (11C1*4C2)/(15C3) = 43/65 = 0.661

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