Combination

Factoral (B = n)
n
∏
i=1
 i Any group of n symbols each with n possible values distributed uniquely. Use this when creating combinations from a given set of objects. AKA: n!
1 2 3 4 5
1 2 6 24 120
A AB ABC ABCD A****
BA ACB ABDC B****
BAC ACBD C****
BCA ACDB D****
CAB ADBC E****
CBA ADCB
B***
C***
D***

1 × 2 × 3 × … n
Combination (B = some K)
n
∏
 
 B Any group of n symbols each with B possible values. Use this when each symbol can be any value (such as number bases). There is no relation between n and B. AKA: Bn
N 8 7 6 5 4 3 2 1
s B7 B6 B5 B4 B3 B2 B1 B0
0 0 0 0 0 0 0 0
B-1: x x x x x x x x

B × B × B × … B (n times)
Combination (B > n)
n-1
∏
i=0
 B-i Any group of n symbols each with B possible values, but each must be unique. Use this when each symbol "consumes" a possible value.
B: 2 3 4 5 6 f
AB AC AD AE AF 1∙0
2 BA BC BD BE BF 2∙1
6 CA CB CD CE CF 3∙2
12 DA DB DC DE DF 4∙3
20 EA EB EC ED EF 5∙4
30 FA FB FC FD FE 6∙5

B × B-1 × B-2 × … B-(n-1)