Tents hold 2,3,5,6, or 12 people. how many combinations of tents are possible to sleep 22 if all tents are fully occupied and exactly one 12 person tent is used

If one 12 person tent is used, the there are 22 - 12 = 10 persons that must be in the other tents.

To place 10 persons in combinations of 2, 3, 5, or 6 you can use:

1)  2 + 3 + 5. = 10  This is a combination of the tents that hold 2, 3, and 5 persons.

2)  You can also use 5 tents of 2 persons: 5 * 2 = 10.

3) You can also use 2 tents of 2 and one tent of 6, because 2* 2 + 6 = 4 + 6 = 10.

4) You can also use 2 tents of 2 and 2 tents of 3: 2 * 2 + 2 * 3 = 4 + 6 = 10.

Those are all the different combinatins possible: 4.

4 different combinations. 
 

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)