Eight people attend the theater "together and sit in a row with exactly eight seats. Suppose the eight people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the eight be seated together in the row"

Question

Arnav Lozano

Mathematics

17 June, 04:30

Eight people attend the theater "together and sit in a row with exactly eight seats. Suppose the eight people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the eight be seated together in the row"

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Answers (1)

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Baron Choi · Answer 1

They can be seated in 120 differents ways.

Step-by-step explanation:

Taking into account that there are 3 couples and every couple has an specific way to sit, for simplify the exercise, every couple is going to act like 1 option and it's going to occupy 1 Place. If this happens we just need to organize 5 options (3 couples and 2 singles) in 5 Places (3 for a couple and 2 for the singles)

It means that now there are just 5 Places in the row and 5 options to organized. So the number of ways can be calculated using a rule of multiplication as:

5 * 4 * 3 * 2 * 1 = 120

1st place 2nd Place 3rd place 4th Place 5th Place

Because we have 5 options for the 1st Place, the three couples and the 2 singles. Then, 4 options for the second Place, 3 options for the third place, 2 for the fourth place and 1 option for the 5th place.

Finally, they can be seated in 120 differents ways.