In the next olympics, the united states can ener 4 athletes in the diving competition. how many different teams of 4 diverscan be selected from a group of 9 divers?
a 36
b 126
c 3024
d 6561
To determine how many different teams of 4 divers can be selected from a group of 9 divers, we can use the combination formula.
The combination formula can be represented as:
C(n, r) = n! / (r! * (n-r)!)
Where:
- n is the total number of divers
- r is the number of divers to be selected
In this case, we have 9 divers and we want to select 4 divers. Therefore, we need to calculate C(9, 4).
Plugging in the values into the combination formula:
C(9, 4) = 9! / (4! * (9-4)!)
Calculating the factorials:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
4! = 4 * 3 * 2 * 1 = 24
(9-4)! = 5!
Simplifying further:
C(9, 4) = 362,880 / (24 * 5!)
Calculating the factorial:
5! = 5 * 4 * 3 * 2 * 1 = 120
Now we can substitute the values into the formula:
C(9, 4) = 362,880 / (24 * 120)
= 362,880 / 2,880
= 126
Therefore, the number of different teams of 4 divers that can be selected from a group of 9 divers is 126. So, the correct answer is option b) 126.