Ariel wants to choose 5 plavers for her basketball team. There are 7 players to choose from. How many different teams can Ariel make?
To solve this problem, we can use the formula for combinations:
nCr = n! / r! (n - r)!
where n is the total number of players (7) and r is the number of players we want to choose for the team (5).
So we can plug in the numbers and simplify:
7C5 = 7! / 5! (7 - 5)!
= (7 x 6 x 5 x 4 x 3) / (5 x 4 x 3 x 2 x 1) (2 x 1)
= 21
Therefore, Ariel can make 21 different teams.
To calculate the number of different teams Ariel can make, we need to find the number of combinations. We can use the combination formula for this:
nCr = n! / (r! * (n-r)!)
Where n is the total number of players (7 in this case) and r is the number of players Ariel wants to choose (5 in this case).
Applying the formula, we get:
7C5 = 7! / (5! * (7-5)!)
= 7! / (5! * 2!)
= (7 * 6 * 5!) / (5! * 2)
= (7 * 6) / 2
= 42 / 2
= 21
Therefore, Ariel can make 21 different teams.
To find the number of different teams Ariel can make, we need to use the concept of combinations.
In this case, Ariel wants to choose 5 players out of a pool of 7 players. The order in which the players are chosen does not matter, as long as she ends up with a team of 5 players.
The formula to calculate the number of combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of players to choose from
- r is the number of players Ariel wants to choose
Let's substitute the values into the formula:
C(7, 5) = 7! / (5!(7-5)!)
Calculating the factorials:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120
(7-5)! = 2! = 2 * 1 = 2
Substituting the factorials back into the formula:
C(7, 5) = 5040 / (120 * 2)
Simplifying:
C(7, 5) = 5040 / 240
Calculating the division:
C(7, 5) = 21
Therefore, Ariel can make 21 different teams with 5 players each from a pool of 7 players.