How many ways can five people, A, B, C, D, and E, sit in a row at a concert hall if C must sit to the right of butnot necessarily next to B?
A) 60
B) 24
C) 20
D) 48

Question

Quizplus · Accepted Answer

To solve this, consider C and B as a single entity since C must be to the right of B. This entity and the three other people (A, D, E) can be arranged in 4! = 24 ways. However, within the BC entity, B and C can switch places, giving us 2! = 2 ways. Multiplying these together gives 24 * 2 = 48 ways. However, the question specifies that C must always be to the right of B, so we don't actually consider the cases where B and C switch places. This means we only consider the initial arrangement of the entities, which is 4! = 24 ways. The mistake in the initial calculation was considering the internal arrangement of the BC entity, which is not needed based on the question's constraints. Therefore, the correct calculation should consider the different ways to arrange the three individuals and the BC pair, which is indeed 4! = 24 ways.

How Many Ways Can Five People, A, B, C, D