I have a number of socks in a drawer. Some of them are red and some of them are blue. If I take out two socks at random, the probability of both socks being red is exactly 1/2, and the probability of both socks being blue is exactly 1/12.
How many socks are in the drawer?
There are 85 red socks and 35 blue socks, giving a total of 120 socks in the drawer.
(85 x 84)/(120 x 119) = (17 x 7)/(2 x 119) = 1/2, as 17 x 7 = 119
(35 x 34)/(120 x 119) = (17 x 7)/(12 x 119) = 1/12, as 17 x 7 = 119