How many different basketball teams of 5 players can be created from a group of 7 players?
C(7,5) = C(7,2) = 7*6 / 1*2 = 21
20
To calculate the number of different basketball teams of 5 players that can be created from a group of 7 players, we can use combination formula.
The formula for combinations is given by:
C(n, k) = n! / (k! * (n-k)!)
Where:
- n is the total number of players in the group (7).
- k is the number of players needed for each team (5).
Using the combination formula:
C(7, 5) = 7! / (5! * (7-5)!)
= 7! / (5! * 2!)
= (7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1 * 2)
= (7 * 6) / 2
= 42 / 2
= 21
Therefore, there are 21 different basketball teams of 5 players that can be created from a group of 7 players.
To find the number of different basketball teams of 5 players that can be created from a group of 7 players, we can use a combination formula. The combination formula is given by:
C(n, r) = n! / (r! * (n-r)!)
Where "n" represents the total number of players to choose from, and "r" represents the number of players needed to form a team.
In this case, we have 7 players to choose from, and we want to create a team of 5 players. Substituting these values into the combination formula, we get:
C(7, 5) = 7! / (5! * (7-5)!)
Calculating this formula:
C(7, 5) = (7 * 6 * 5!) / (5! * 2!)
The factorials in the numerator and denominator cancel out, leaving us with:
C(7, 5) = (7 * 6) / 2!
Further simplifying:
C(7, 5) = 42 / 2
C(7, 5) = 21
Therefore, there are 21 different basketball teams of 5 players that can be created from a group of 7 players.