Question

A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, isto be chosen from a group of 5 Republicans, 6 Democrats, and 4 Independents. Howmany committees are possible?

Answer 1

$\fontsize{18}{10}{\textup{\textbf{The number of possible committees is 600.}}}$

Step-by-step explanation:

There are 5 Republicans, 6 Democrats and 4 Independents, out of which we are to choose a committee of 7, consisting of 2 Republicans, 2 Democrats and 3 Independents.

We have

Number of ways of choosing 2 Republicans out of 4 Republicans is given by

$n_1=^5C_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5\times4}{2\times1}=10.$

Number of ways of choosing 2 Democrats out of 6 Republicans is given by

$n_2=^6C_2=\dfrac{6!}{2!(6-2)!}=\dfrac{6\times5}{2\times1}=15.$

Number of ways of choosing 3 Independents out of 4 Independents is given by

$n_3^4C_3=\dfrac{4!}{3!(4-3)!}=4.$

Therefore, the number of ways in which the committee of 7 is formed is

$n_1\times n_2\times n_3=10\times15\times4=600.$

Thus, the required number of ways is 600.

#Learn more

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