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?
So we are asked - what is probability of selecting 2 boys and 2 girls right:
We were not told about the actual selection, hence Before finding the probability, we should find what the different ways in which we can select 4 children.
So select 1 boy, then 1 boy, then 1 girl and then 1 girl or you can also select 1 B, 1 G, 1 B and 1 G.
Basically selecting 4 from BBGG. ie. 4 * 3 * 2 *1 / (2! * 2!) ways of making the selection. = 6.
Probability of selecting 1st boy = 3/6
Probability of selecting 2nd boy = 2/5 (as we have already selected one boy above)
Probability of selecting 1st Girl = 3/4
Probability of selecting 2nd Girl = 2/3
Multiply all of above with different ways of selecting the children =
P (selecting 2 boys and 2 girls) = 3/6 * 2/5 * 3/4 * 2/3 * 6 = 3/5
Answer : D