If there are 4 projects A B C and D but C D cannot be in th

If there are 4 projects, A, B, C and D, but C & D cannot be in the same bundle, how many different combinations could you make?

Solution

There are 4 projects, A, B, C and D

C and D cannot be together.

Hence combinations are Total - no of ways when C and D are together.

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For C and D to be together we can take CD as a single unit, we have 3 projects

They can be arranged in 3! ways. C,D between them can be arranged in 2! ways

Hence total no of ways for C, D together =2(3!)

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Different combination where C and D not together = 4!-2(3!)

= 24-12 = 12 ways.