A customer ordered sixteen zingers. Zingers are placed in packages of​ four, three, or one. In how many different ways can this order be​ filled?

1 Answer
SCooke
Apr 27, 2018

17

Explanation:

The order doesn't matter, only the number, so it is a combination instead of a permutation. Requiring a particular sum makes it trickier.
#16 = 1x + 3y + 4z#
Table of Possible Values (17):
x y z
1 5 0
4 4 0
7 3 0
10 2 0
16 0 0
0 4 1
3 3 1
6 2 1
9 1 1
12 0 1
2 2 2
2 2 2
5 1 2
8 0 2
1 1 3
4 0 3
0 0 4

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