Discussion
A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is
Answer: C
Count all pairs, then remove those that break the rule.
\[ \text{total} = {}^{5}C_{2} = 10 \]
Invalid pairs are those containing Mathematics 2 without Mathematics 1 - that is, Mathematics 2 paired with commerce, economics or statistics:
\[ 3 \text{ invalid pairs} \]
\[ 10 - 3 = 7 \]
The pair {Mathematics 1, Mathematics 2} is allowed, since the prerequisite is satisfied within the pair itself.
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