JAMB Mathematics 2021 Paper

Concept:When two numbers are removed without replacement, count the distinct possible pairs and the favourable pairs with an even sum.Explanation:The available numbers are $\{1, 2, 3, 4\}$.Two different numbers are removed, so the total possible pairs are $\binom{4}{2} = 6$.The possible pairs are:$(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)$.Their sums are:$3, 4, 5, 5, 6, 7$.The even sums are $4$ and $6$.Thus, the favourable pairs are $(1,3)$ and $(2,4)$, giving $2$ favourable outcomes.So the probability is:$P(\text{even sum}) = \frac{2}{6} = \frac{1}{3}$.Answer:$\frac{1}{3}$This is Option C.