Question

Question #033a1

Answer 1

The committee can be selected in `2016` ways.

Explanation:

We have a group of 12 people: 8 women and 4 men.
First we have to choose 3 women. We can do it in `C""_8^3` ways, which can be calculated as:

`C""_8^3=(""_3^8)=(8!)/(3!*5!)=(6*7*8)/6=56`

Now we have to select remaining 2 members from all remaining people (9) (they can be either men or women). The number of possible choices can be calculated as:

`C""_9^2=(""_2^9)=(9!)/(2!*7!)=(8*9)/2=4*9=36`

To calculate final result we have to multiply the results above.

`n=C""_8^3*C""_9^2=56*36=2016`