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Nawaryi · Nov 14, 2011, 06:47 AM

From 6 biologists and 7 chemists a committee of 3 biologists and 3 chemists are to be formed. How many committee can be formed if no restrictions are imposed?
a) 20
b) 35
c) 700
d) 25,200
e) none of the choices.

ebaines · Nov 14, 2011, 07:19 AM

Are you familiar with combinations? If you have a group of A objects (or people as in this case) you can select B of them in C(A,B) ways, where

$<br /> C(A,B) = \frac {A!} {(A-B)! B!}<br />$

So for example for committee of 3 people from a pool of 8 can be selected is:

$<br /> \frac { 8!} {5!3!} = \frac {8 \times 7 \times 6} {3 \times 2 \times 1 } = 56$
ways.

So for your problem use combinations to figure out how many different ways the biologists can be selected and multiply by how many different ways the chemists can be selected.