# Algebra

posted by .

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!).

## Similar Questions

1. ### math

A total of four students belong to all three teams, the baseball, basketball and football team. These four students represent 10% of the baseball team, 25% of the basketball team and 8 1/3 % of the football team. There are 20 students …
2. ### phi103

21{1[2(24)24]}> The average height of members of the high school basketball team is six feet, three inches. Jerry is on the high school basketball team, so Jerry must be taller than six feet. The argument above is flawed because …
3. ### Algebra 1

Andrea, Betty, Joyce, Karen, and Paula are starters on their school basketball team. How many different groups of three can be chosen for a newspaper photo?
4. ### algebra

Andrea Betty Joyce Karen and Paula are starters on their school basketball team . How many different groups of three can be chosen for a photo?
5. ### logic

the average height of members of the high school basketball team is six feet,three inches . jerry is on the high school basketball team, so jerry must be taller than six feet. the argument above is flawed because it confuses
6. ### english

The average height of members of the high school basketball team is six feet, three inches. Jerry is on the high school basketball team, so Jerry must be taller than six feet. The argument above is flawed because it confuses
7. ### algebra

The coach of a soccer team is holding tryouts and can take only 3 more players for the team. There are 6 players trying out. How many different groups of 3 players could possibly be chosen?
8. ### Algebra

The coach of a soccer team is holding tryouts and can take only 3 more players for the team. There are 5 players trying out. How many different groups of 3 players could possibly be chosen?
9. ### Algebra

The coach of a soccer team is holding tryouts and can take only 3 more players for the team. There are 5 players trying out. How many different groups of 3 players could possibly be chosen?
10. ### Algebra

The coach of a soccer team is holding tryouts and can take only 2 more players for the team. There are 8 players trying out. How many different groups of 2 players could possibly be chosen?

More Similar Questions