How many different ways can you score 10 points in a basketball game?

How many different ways can you score 10 points in a basketball game?

I counted 14, but I'm not sure if I am missing one.How many different ways can you score 10 points in a basketball game?
Doing it in an orderly fashion is the best way to see you got them all.

Use higher numbers as much as possible, then go to lower ones.



3 3 3 1

3 3 2 2

3 3 2 1 1

3 3 1 1 1 1

3 2 2 2 1

3 2 2 1 1 1

3 2 1 1 1 1 1

3 1 1 1 1 1 1

---- that exhausts the 3's ---

2 2 2 2 2

Then can replace each of the 2's with 1 1 (5 more ways)

--- that takes care of the 2's ---

all 1's



Summary:

8 using 3's 2's and 1's

5 using 2's and 1's

1 using all 1's



Total 14.

.How many different ways can you score 10 points in a basketball game?
You can have 3 points, 2 points or 1 point

10 = 2+2+2+2+2

10 = 3+3+2+2

10 = 1+3+3+3

10 = 3+3+2+1+1

10 = 3+3+1+1+1+1

10 = 3 + 2+2+2+1

10 = 3+2+2+1+1+1

10 = 3+2+1+1+1+1+1

10 = 3+1+1+1+1+1+1+1

10 = 2+2+2+2+1+1

10 = 2+2+2+1+1+1+1

10 = 2+2+1+1+1+1+1+1

10 = 2+1+1+1+1+1+1+1+1

10 = 1+1+1+1+1+1+1+1+1+1

This is 14 indeed if the order plays no role.

If you have to take the order into account,

the number of possibilities is much bigger.

How many different ways can you score 10 points in a basketball game?
yes 14 is right