Arrange balls in bins

Row\Col	B	C	D	E	F
2	Balls	Bins
3	20	4
4	# Arrangements
5	969
6
7	Arr #	Bin 1	Bin 2	Bin 3	Bin 4
8	1	17	1	1	1
9	2	16	2	1	1
10	3	16	1	2	1
11	4	16	1	1	2
12	5	15	3	1	1
13	6	15	2	2	1
14	7	15	2	1	2
15	8	15	1	3	1
16	9	15	1	2	2
17	10	15	1	1	3
18	11	14	4	1	1
19	12	14	3	2	1
20	13	14	3	1	2

See the workbook at https://app.box.com/s/d6mo50rxjiipx01xj9sv15soh8rna8nd

The genesis of the formula is this:

Imagine N balls in a row. You can insert a divider between any two adjacent balls to partition them into bins. To create M bins, you need M-1 dividers, and there are N-1 slots to choose from. So =COMBIN(N-1, M-1) gives the number of arrangements.