Hints and solutions to
Make a List #10

How many different ways is it possible to score 15 points in basketball?
Remember, in basketball you can score 1 point (for a foul shot), 2 points (for a "regular" basket), or 3 points (for a "long" basket) at a time.

In this problem, we're not interested in the order in which the points were scored, just how many foul shots, how many regular baskets, and how many 3-point shots were made (in other words, we're interested in the "box score").
For instance, you could score four 2-pointers, two 3-pointers and one foul shot, or three 2-pointers, one 3-pointer and six foul shots, and so forth.
This definitely calls for one of our famous lists!

Long baskets
Regular baskets
Foul shots

5
0
0

4
1
1

4
0
3

3
3
0

3
2
2

3
1
4

3
0
6

2
4
1

2
3
3

2
2
5

2
1
7

2
0
9

1
6
0

1
5
2

1
4
4

1
3
6

1
2
8

1
1
10

1
0
12

0
7
1

0
6
3

0
5
5

0
4
7

0
3
9

0
2
11

0
1
13

0
0
15

To count these quickly, notice the pattern in the long basket column. There is one 5, then two 4's then four 3's then five 2's, then seven 1's then eight 0's.
So altogether there are 1+2+4+5+7+8 = 27 different ways to make 15 points in basketball.