more permutations...

Hi,
Let Ben and Sheryl be grouped together. So, we have 3 persons +1 group of Ben and Sheryl.
So, they can be arranged in 4! ways
group of Ben and Sheryl can be permuted in 2! ways
So, number of ways in 4!*2! = 48 ways
Now, these include Bryan and David together as well.
Let's consider the case of Bryan and David together as well. So we make them a group.
Number of ways is 3!*2!*2! = 24ways
So, for them not to be together, the number of ways is 48-24 = 24ways.

(OR)

Jane, Bryan, Sheryl, David and Ben went to a concert. Ben has a crush on Sheryl,
Consider __ Jane__(Ben+Sheryl)__
Jane and (Ben+Sheryl can be arranged in 2!*2! = 4 ways.
There are 3 gaps in which David and Bryan can be filled.
This can be done in 3P2 = 6 ways.
So, total number of ways is 4*6 = 24 ways

questions like there you should use symmetry.

Ben and Sheryl sit together.

total people 4 (Be-Sh one group)
also Be-SH can sit in 2! ways

thus total ways = 2!*4! = 48.
in half if these 48 cases D and Br will sit apart and in half they will sit together.

thus total cases = 48/2 = 24.

amit2k9 wrote: in half if these 48 cases D and Br will sit apart and in half they will sit together.

thus total cases = 48/2 = 24.

why half the cases? please explain