you want to pick a four-player tennis team there are eight players to choose from.how many different teams can you form?
A)70
B)1,680
C)48
D)336
*plz jus help me or show me how to do it*
that would be 8 - choose - 4
= C(8,4) = 8!/(4!4!)
= 70
To find the number of different teams you can form for a four-player tennis team from a pool of 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 to choose from (in this case, 8),
- r is the number of players needed for a team (in this case, 4), and
- ! represents the factorial operation (e.g., 4! is equal to 4 x 3 x 2 x 1).
Applying the formula to the given scenario, we have:
C(8, 4) = 8! / (4!(8-4)!)
= 8! / (4!4!)
Calculating further, we have:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
Plugging in the values, we get:
C(8, 4) = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1)(4 x 3 x 2 x 1))
Simplifying the expression:
C(8, 4) = 70
So, the number of different teams you can form is 70.
The correct answer is A) 70.
To determine how many different teams can be formed from a group of eight players, we can use the combination formula. The formula for combination is:
C(n, r) = n! / (r! * (n - r)!)
Where:
- C(n, r) denotes the combination of selecting r items from a set of n items
- n! represents n factorial, which is the product of all positive integers less than or equal to n
In this case, we need to select 4 players from a group of 8, so n = 8 and r = 4. Plugging these values into the combination formula, we have:
C(8, 4) = 8! / (4! * (8 - 4)!)
Calculating the factorial terms:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
4! = 4 * 3 * 2 * 1 = 24
(8 - 4)! = 4! = 24
Now substitute these values back into the combination formula:
C(8, 4) = 40,320 / (24 * 24)
Simplifying:
C(8, 4) = 40,320 / 576
C(8, 4) = 70
Therefore, the answer is A) 70.