Maths Question?

Question

If you have a class consisting of 10 girls and 20 boys, in how many different ways can you form a committee from the class members such that there will be 2 girls and 2 boys on the committee?

1. 50
2. 8,550
3. 34,200
4. none of the above

Answer 1

10 x 9 / 2 x 19 x20 /2 = 8550

Answer 2

Assuming your committee is made up of four class members, you have (10 choose 2) = 10*9/2 = 45 ways to choose the girls and (20 choose 2) = 20*19/2 = 190 ways to choose the boys. This gives a total of 45*190 = 8550 such committees.

Answer 3

The important word in the question is DIFFERENT.

Now there are 10 girls to choose from and you need 2. So, by the counting rule, you get 10*9. But say you chose girl 1 for the first position and girl2 for the first position, the 10*9 includes girl2 in first position and girls 1 in 2nd position so you have to divide by 2.

Now, for the boys it is 20*19 and by the same logic, divide by 2.
and you get 45 * 190 or 8,550.

Answer 4

First you pick a girl... you have 10 to choose form
Then you pick anther girl.... from the 9 left
Then you pick a boy.... from the 20 there
then you pick another boy.... from the 19 left.

So 10 X 9 X 20 X 19.

You do the Math.