From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?
First we need to find the total number of possible groups:
6C4 (6 total children, picking a group of 4) = 6!/(4!*2!) = 15
So there are 15 different groupings possible.
Now we need to find out how many different groups there are with 2 boys and 2 girls. To get these groups, we need to pick 2 out of the 3 boys and 2 out of the 3 girls. So we need to know how many different ways you can select the two boys and how many ways you can select the 2 girls and multiply those together to get total number of possible groups... So:
3C2 * 3C2 = 3!/(2!*1!) * 3!/(2!*1!) = 3*3 = 9
Therefore: 9/15 = 3/5 or 60%
