Tents hold 2, 3, 5, 6, or 12 people. How many combinations of tents are possible...

Question

Tents hold 2, 3, 5, 6, or 12 people. How many combinations of tents are possible to sleep 20 if all tents are fully occupied and exactly one 12-person tent is used?

 

I'm very confused. 

Could someone please explain how I am supposed to figure this out?

Thanks.

Answer 1

"sleep 20 if all tents are fully occupied"   means that there are 20 total people in groups of 2, 3, 5, 6, or 12.

 

"exactly one 12-person tent is used" means that there is one tent with 12 people and 8 people in other tents.

 

The problem may now be restated:

   "How many combinations of 2, 3, 5 or 6 can add up to 8 ??

 

Well, there is:

    2 + 6 = 8

    2 + 3 + 3 = 8

    2 + 2 + 2 + 2 = 8

    3 + 5 = 8

 

So, there are four possible combinations (order does not matter) of tents:

    2, 6, 12

    2, 3, 3, 12

    2, 2, 2, 2, 12

    3, 5, 12

Answer 2

If a 12 person tent is used then 8 people must be tented in the others.

So how many different combinations of 2, 3, 5, and 6 can be used?

6 + 2

3 + 3 + 2

5 + 3

2 + 2 + 2 + 2