SOLUTION: I need to figure out how many possible milkshake combinations there can be with 64 ingredients. No ingredient can be used more than once in a combination and there is a max of 5 i

Question 163408: I need to figure out how many possible milkshake combinations there can be with 64 ingredients. No ingredient can be used more than once in a combination and there is a max of 5 ingredients per combination.
Thanks for your help.
Found 2 solutions by ankor@dixie-net.com, Levski123:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I need to figure out how many possible milkshake combinations there can be with 64 ingredients. No ingredient can be used more than once in a combination and there is a max of 5 ingredients per combination.
:
How about:
Five ingredients
64 * 63 * 62* 61 * 60 = 914,941,440
Four ingredients
64 * 63 * 62* 61 = 15,249,024
Three ingredients
64 * 63 * 62 = 249,984
Two ingredients
64 * 63 = 4032
1 ingredient
64
:
Add em up and you get: 930,444,544 combinations

Answer by Levski123(6) (Show Source): You can put this solution on YOUR website!
The question asks for combinations not permutations, so the answer will be 64C5
OR
n!/(n-r)!r!
64!/(64-5)!5!
64x63x62x61x60/ 120
= 7,624,512
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