Thank you all.
@whale-av
@ben.wes
How would you implement the combinations formula (C (n, r) = n!/r! (n-r)!) in an efficient way? So that an n and r can be entered in and print all possible combinations?
I used the factorial expression object to calculate the combinations formula using- expr (fact($f1)) / ((fact($f2)) * (fact($f1 - $f2)))
What approach would you take to calculate the combinations formula without using the expressions object?
What approach would you take to calculate the combinations formula with using the expressions object?

Adding a List and or Array
How would you approach being able to add any type of customizable list/array (for example, list/array = A, B, C, D, E, F) and then telling the patch you want to generate any type of combination and then print all possible combinations?
For example, customizable list/array = A, B, C, D, E, F (n)
generate all possible combinations of 2 (r) also customizable
Print-
All possible combinations = 15
A, B
A, C
A, D
A, E
A, F
B, C
B, D
B, E
B, F
C, D
C, E
C, F
D, E
D, F
E, F

fac.pd
I built a patch that is supposed allow you to enter in a number and calculate the factorial (without using the expressions object).
Factorial of n = n! = n × (n – 1) × (n – 2) × … × 1
Example 5! is 5 × 4 × 3 × 2 × 1 = 120

I used this max msp factorial patch as a guide.

Looking for assistance in making the factorial patch in Pure Data as efficient as possible.
I want to build this patch using Pure Data primitives instead of using the expression object.

Please note that there is a discussion here that using float values instead of integers allows the recursive method for calculating factorials to have higher input values before failure.
https://cycling74.com/forums/recursive-factorial-function-limits