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KATRIN_1 [288]
3 years ago
5

Eight people attend the theater "together and sit in a row with exactly eight seats. Suppose the eight people consist of three m

arried 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"
Mathematics
1 answer:
Nata [24]3 years ago
8 0

Answer:

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:

<u>      5         </u>*<u>        4          </u>* <u>       3           </u> *  <u>        2     </u>  * <u>         1         </u> = 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.

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