Question

Twelve individuals want to form a committee of four. (a.) How many committees are possible? (b.) The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many committees consisting of 1 biologist, 1 chemist, and 2 physicists are possible? (c.) In the setting of part (b), if all committees are equally as likely, what is the probability the committee formed will consist of 1 biologist, 1 chemist, and 2 physicists?

          Twelve individuals want to form a committee of four.

(a.) How many committees are possible?
(b.) The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many
committees consisting of 1 biologist, 1 chemist, and 2 physicists are possible?
(c.) In the setting of part (b), if all committees are equally as likely, what is the
probability the committee formed will consist of 1 biologist, 1 chemist, and 2
physicists?

Twelve individuals want to form a committee of four.

(a.) How many committees are possible?
(b.) The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many
committees consisting of 1 biologist, 1 chemist, and 2 physicists are possible?
(c.) In the setting of part (b), if all committees are equally as likely, what is the
probability the committee formed will consist of 1 biologist, 1 chemist, and 2
physicists?

Added by Ivan H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

02/24/2023

Step 1

This can be calculated using the formula for combinations, which is: $$C(n, k) = \frac{n!}{k!(n-k)!}$$ In this case, n = 12 (total number of individuals) and k = 4 (number of individuals in the committee). So, the number of possible committees is: $$C(12, 4) = Show more…

Show all steps

Thanks for your feedback!

Twelve individuals want to form a committee of four. (a.) How many committees are possible? (b.) The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many committees consisting of 1 biologist, 1 chemist, and 2 physicists are possible? (c.) In the setting of part (b), if all committees are equally as likely, what is the probability the committee formed will consist of 1 biologist, 1 chemist, and 2 physicists?