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

Question

In how many ways can 8 people be seated on a bench if 3 particular people must sit together?

Answer 1

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