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10 college friends decide to go camping. Luisa and Paola go on the condition that they will always stay in the same tent. If the friends have 3 tents with capacities of 2, 3 and 5 people, respectively, in how many ways can they be distributed in the tents?

Respuesta :

Tent of 5 people

Find out the combination 3C8 (Luisa and Paola have already placed them in the tent.)

so

[tex]3C8=\frac{8!}{3!(8-3)!}=56[/tex]

Tent of 3 people

Find out the combination 1C8 (Luisa and Paola have already placed them in the tent.)

C8=8

Tent of 2 people ------> only one combination

so

the number of ways is

(56)(8)(1)=448 ways

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