This question doesn't make any sense, at least if the OA is A. I can guess the logic they use to justify 'A' as the right answer -- using only Statement 1, there are only two primes that sum to 12, namely 5 and 7. If we want to seat 5 people in 7 chairs, there are 7*6/2! = 21 ways to choose the two empty chairs (we divide by 2! because the order of the 2 empty chairs doesn't matter), then 5! ways to arrange the people in our chosen chairs. Multiplying those two numbers gives the total. I'm sure they then claim that when we want to seat 7 people in 5 chairs, there are 7*6/2! ways to choose the two unused people, and again 5! ways to arrange them, so I imagine they claim the answer to either question is (7*6/2!)*5! = 2520.
But if you're asked "in how many ways can you seat 7 people in 5 chairs", the answer is "you can't -- you don't have enough chairs". The answer to that question is not 2520, unless you're misusing language. They mean to ask something more like "How many different seating arrangements could result when x people are seated in y chairs (if some of the people need not be seated at all)", but then the parenthetical comment would give away the 'trick' they're trying to use.
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