6. Six people attend the theater together and sit in a row with exactly six seat

Question

6. Six people attend the theater together and sit in a row with exactly six seats between two aisles a) How many ways can they be seated together? b) Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people seated together in the row with the doctor in an aisle seat? c) Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row? d) Solve part c) but without the restriction that the husband must sit on the left. That is, how many ways can the six be seated together so that every couple is siting next to each other?

Explanation / Answer

Ans 6

a)

In 6! ways = 720 ways

b)

2* 5! ways = 240 ways

c)

Couples can be treated as a single group . so we have 3 groups

3! ways = 6 ways

d)

Each group can have 2 ways (husband on left or husbamd on right)

6*2*2*2 = 48 ways

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