A tiffin box contains 'a' pink and (a - 4) yellow toffees, and another tiffin box contains (a - 1) yellow and (a - 3) pink toffees. If one of the tiffin boxes is selected at random and 2 toffees are drawn at random from it, the probability that the two toffees are of different colors is 67132. Find the total number of toffees in the first tiffin box.

A box contains 'x + 4' red, 'x – 1' green and 'x – 5' blue balls. If two balls are drawn from the bag one after another without replacement, then the probability of getting one red and one green ball is equal to the probability of getting a sum equal to or more than 8 when two fair dice are rolled. Find the probability of drawing a red ball when one ball is drawn at random from the bag.

Four persons are chosen at random from a group containing 3 men, 2 women, and 4 children. The probability that exactly two of them are children is: