# Algebra

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Andrea, Kate, Verona, Beverely, Karen, Joanna, George, and Paula are starters on their school basketball team. How many different groups of three can be chosen for a newspaper photo?

• Algebra - ,

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

• Algebra - ,

What do you mean by C(8,3) ? What does the exclamation point mean?

• Algebra - ,

C(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 - ,

Thank you for the explanations!
I also have another question. Where did the 5! came from?

• Algebra - ,

5! 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!).