Ariel wants to choose 5 players for her basketball team. There are 7 players to choose from. How many different teams can Ariel make?
A. 21
B. 32
C. 42
D. 56.
AAAaannndd the bot gets it wrong yet again!
7C5 = 7*6 / 1*2 = 21
so, A
56 = 8P2
I'm sorry for the mistake in my previous response. You are correct that the correct answer is A, 21. The number of ways to choose 5 players from a group of 7 is given by the combination formula:
7C5 = 7! / (5!2!) = (7*6)/(2*1) = 21.
Thank you for catching the error and providing the correct solution.
To calculate the number of different teams Ariel can make, we need to use the combination formula.
The formula for combination is given by:
C(n, r) = (n!)/(r!(n-r)!)
Where n is the total number of players available to choose from, and r is the number of players Ariel wants to choose.
In this case, n = 7 (total number of players available) and r = 5 (number of players Ariel wants to choose).
Let's substitute these values into the formula:
C(7, 5) = (7!)/(5!(7-5)!)
Simplifying further:
C(7, 5) = (7!)/(5!2!)
Now, let's calculate the factorial values:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
5! = 5 x 4 x 3 x 2 x 1 = 120
2! = 2 x 1 = 2
Substituting these factorial values into the formula:
C(7, 5) = (5040)/(120 x 2) = 5040/240 = 21
Therefore, Ariel can make 21 different teams.
The answer is A. 21.