JAMB 1990 · UME · Q49

Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?

Worked solution (try it first)

List the pairs: $\{1, 2\}, \{1, 3\}, \{1, 4\}, \{2, 3\}, \{2, 4\}, \{3, 4\}$ , which is 6 pairs.
An even sum needs two odds or two evens: only $\{1, 3\}$ and $\{2, 4\}$ .
So the probability is $\frac26 = \frac13$ , option C.