In how many ways can 5 people sit in a row if two specific people must not sit together?
I know the total arrangements are 5! = 120. But I am confused about how to calculate the arrangements where the two specific people ARE together and then subtract. Can you walk me through it?
1 Answer
RJRahul Joshi
✓ Accepted
· 15d ago
▲ 12
Total arrangements: 5! = 120. Now count arrangements where the two specific people (call them A and B) are together: treat AB as one unit, giving 4 units. Arrangements of 4 units: 4! = 24. But A and B can swap within the pair: multiply by 2 = 48. So arrangements where they sit together = 48. Required answer: 120 - 48 = 72.
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