MHTCET 15 May 2024 Shift 2 Paper

Concept:Since at least one question must be chosen from each of the 3 sections, the 5 selected questions can be distributed among the sections only in these two patterns: $(1,1,3)$ or $(1,2,2)$, taken in all possible orders.Explanation:There are 3 sections, each having 5 questions.For the distribution $(1,1,3)$: the number of ways is $\binom{5}{1}\binom{5}{1}\binom{5}{3} = 5 \times 5 \times 10 = 250$.The section that gets 3 questions can be any of the 3 sections, giving $3 \times 250 = 750$ ways.For the distribution $(1,2,2)$: the number of ways is $\binom{5}{1}\binom{5}{2}\binom{5}{2} = 5 \times 10 \times 10 = 500$.The section that gets 1 question can be any of the 3 sections, giving $3 \times 500 = 1500$ ways.Therefore, total number of ways $= 750 + 1500 = 2250$.Answer:$2250$, which is option D.