how many different 5 player teams can be chosen from eight players? What formula do I use to solve this?
The number of combinations can be found from the formula
C(n,r)=n!/(r!(n-r)!)
n=total number of distinct objects
r=size of sample
For example,
there are 9 different fruits to choose from. The number of different samples of 6 fruits is equal to C(9,6)=9!/(6!(9-6)!)
=84
C(8,5)=8!/(5!(8-5)!) So do I * these numbers next to come up with the answer I got 120
Yes, basically that, but watch out for parentheses and order of operations.
Examples:
C(8,5)=8!/(5!(8-5)!)
=40320/(120*6)
=56
and
C(9,6)=9!/(6!(3!))
=362880/(720*6)
=84
To find the number of different 5-player teams that can be chosen from eight players, you can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n is the total number of players
- r is the number of players in each team
- "!" represents factorial.
In this case, you want to find the number of different 5-player teams chosen from 8 players, so you would use the formula as follows:
C(8, 5) = 8! / (5! * (8 - 5)!)
Now, let's compute it step-by-step:
1. Calculate the factorial of the total number of players, 8! (8 factorial).
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
2. Calculate the factorial of the number of players in each team, 5! (5 factorial).
5! = 5 * 4 * 3 * 2 * 1 = 120
3. Calculate the factorial of the difference between the total number of players and the number of players in each team, (8 - 5)!, which is 3! (3 factorial).
3! = 3 * 2 * 1 = 6
4. Substitute these values into the combination formula:
C(8, 5) = 40,320 / (120 * 6)
5. Simplify the expression:
C(8, 5) = 66
Therefore, there are 66 different 5-player teams that can be chosen from eight players.