Tents hold 2, 3, 5, 6, or 12 people. how many combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.

12

Step-by-step explanation:

We are given that tent hold 2,3,5,6 or 12 people.

We have to find the combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.

If one 12 person tents is used then remaining people=32-12=20

Therefore, 20 people that must be in other tents.

To place 20 persons in combination of 2,3,5 and 6.

20=5+5+5+5

20=5+5+5+2+3

20=6+6+6+2

20=2(10)=2+2++2(10 times)

20=5+5+2(5)(5 times add 2)

20=6+6+2(4) (4 times add 2)

20=3+3+3+3+3+3+2

20=3+3+3+3+3+5

20=3+2+6+5+2+2

20=3+3+3+3+6+2

20=3+3+5+5+2+2

20=6+6+3+5

Hence, there are 12 possible combination of tents  to sleep 32  all tents are fully occupied and exactly one 12 person tents is used.