Discussion
Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
Answer: C
There are 6 arrangements.
Four people can sit in 4! = 24 ways. Treat P and R as a block to count the arrangements where they are adjacent: 3! × 2 = 12. So 24 - 12 = 12 arrangements keep P and R apart.
In any arrangement, S is either to the right of Q or to the left, and swapping S and Q turns one case into the other without affecting whether P and R are adjacent. So exactly half of the 12 have S to the right of Q, giving 6.
12 forgets the condition on S and Q, and 8 is not a possible count. 2 is the count if S must sit immediately to the right of Q, which the question does not require.
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