Question

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?

Answer 1

Tent of 5 people

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

so

`3C8=(8!)/(3!(8-3)!)=56`

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