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In how many ways can a committee of three men and two women be formed from a group of eight men and seven women?

Sagot :

By counting principle rule, we have

[tex]\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}[/tex]

Then the ways a committee of three men and two women can be formed is

[tex]\binom{8}{3}\cdot\binom{7}{2}=1176[/tex]

Therefore, there are 1176 possible ways.

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