I have x pairs of red socks and y pairs of green socks to wear for (x+y) days.
How many ways can you wear these socks (one pair each day)? For example, first day : green, second : green, third: red ...
(Note: you cannot mix colors! That is, you can't wear one green sock and one red sock on each foot)
Simply, $$\binom{x+y}{x}$$ All you are doing is choosing the days that you are wearing red socks: there are $x+y$ total socks (same as the number of days), and the other days you must wear green. Similarly, $$\binom{x+y}{y}$$ In the case, out of the total number of socks/days, you are picking the green socks to wear.