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December 9, 2016
Posted by **Anonymous** on Monday, May 28, 2012 at 3:56pm.

- Algebra -
**MathMate**, Monday, May 28, 2012 at 8:50pm8 choose 3 = C(8,3)=8!/(3!5!)

- Algebra -
**Anonymous**, Monday, May 28, 2012 at 9:28pmWhat do you mean by C(8,3) ? What does the exclamation point mean?

- Algebra -
**MathMate**, Monday, May 28, 2012 at 10:35pmC(8,3) is the function that represents the number of ways to choose 3 items out of 8. C is short for combination.

8! is a math function call 8 factorial, and stands for the product 8*7*6*5*4*3*2*1=40320

3!=3*2*1, etc.

What C(8,3) means is that to choose 3 people, we would have a choice of 8 candidates for the first one, 7 candidates for the second, and 6 candidates for the third.

However, to choose the same 3 candidates, we could choose them in 6 different orders, namely ABC, ACB, BAC, BCA, CAB, CBA, or 3! ways.

So 8*7*6=8!/5!, but we have to divide by 3! in order not to over-count by 6 times, so we divide by 3! to get 8!/(5!3!). - Algebra -
**Anonymous**, Thursday, May 31, 2012 at 12:00amThank you for the explanations!

I also have another question. Where did the 5! came from? - Algebra -
**MathMate**, Thursday, May 31, 2012 at 7:30am5! comes from 8-3.

The general formula for C(n,r) is

C(n,r)=n!/(r!(n-r)!)

So if n=8, r=3, n-r=5, and

C(8,3)=8!/(3!5!)

You will notice that by symmetry,

C(8,3)=C(8,5) because they both equal 8!/(3!5!).