SOLUTION: Permutations, combinations, and the multiplication principle for counting. 12c 4 12/4= 12/4/8=165 11c 3 =11/3 11/3/8=495 I am needing a better explanation on how the answer c

Question 1089759: Permutations, combinations, and the multiplication principle for counting.
12c 4 12/4= 12/4/8=165
11c 3 =11/3 11/3/8=495
I am needing a better explanation on how the answer comes up to 165 and how they got 495 please show me all the steps I am missing something
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
It seems like the two values have been mixed up somehow.

Here's what it should be:

n C r = (n!)/(r!*(n-r)!)
12 C 4 = (12!)/(4!*(12-4)!)
12 C 4 = (12!)/(4!*8!)
12 C 4 = (12*11*10*9*8!)/(4!*8!)
12 C 4 = (12*11*10*9)/(4!)
12 C 4 = (12*11*10*9)/(4*3*2*1)
12 C 4 = 11880/24
12 C 4 = 495

n C r = (n!)/(r!*(n-r)!)
11 C 3 = (11!)/(3!*(11-3)!)
11 C 3 = (11!)/(3!*8!)
11 C 3 = (11*10*9*8!)/(3!*8!)
11 C 3 = (11*10*9)/(3!)
11 C 3 = (11*10*9)/(3*2*1)
11 C 3 = 990/6
11 C 3 = 165

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First of all, you have the answers backwards. 12 choose 4 is 495 and 11 choose 3 is 165.

12 choose 4:

You can figure the other one on your own.

John

My calculator said it, I believe it, that settles it

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