Answer to Question #90294 in Combinatorics | Number Theory for Michael

Question #90294
In how many ways can 8 people be seated on a bench if 3 particular people must sit together?
1
Expert's answer
2019-05-28T03:53:45-0400

Solution:

If there are 8 people and 3 need to sit next to each other you have 6 groups to seat. The 5 who are don’t care and 3 who need to sit together.

Ways to seat 6 groups:


"P_6 = 6!"

3 people who need to seat together can sit in:


"P_3 = 3!"

ways.

So total number of ways:


"P_{total} = P_6 * P_3 = 6! * 3! = 720 * 6 = 4320"

Answer: 4320


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