1) Amy, Brian, Cheryl, Danny and Eric went to a concert. How many arrangements are possible when they sit in five adjacent seats if Brian refuses to sit next to Danny?
The answer is 72.
2006-12-10 22:43:49 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The total number of arrangements without any restrictions is 5! or 120. Now we need to subtract off the arrangements where Brian and Danny are next to each other. They could be next to each other in positions:
12
23
34
45
and in either order in those positions.
So that is 2x4 = 8 permutations.
For each of permutations, the others could be in any of 3! = 6 arrangements.
So 5! - 2x4x3! = 120 - 48 = 72
2006-12-10 22:58:39 · answer #1 · answered by Northstar 7 · 1⤊ 0⤋
total no of arrangements is 5! = 120 (without condition)
no of ways they can sit together is 48
thus total arrangement is 120-48=72
2006-12-11 07:26:44 · answer #2 · answered by Anonymous · 0⤊ 0⤋