A baseball team has 4 infielders and 6 outfielders. How many ways can four fielders be sent in a game consisting of 2 infielders and 2 outfielders?
4c2*6c2
To find the number of ways to select four fielders for a game consisting of 2 infielders and 2 outfielders, you can use the concept of combinations.
First, let's calculate the number of ways to select 2 infielders from the 4 available infielders. This can be done using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of objects (in this case, the number of infielders available) and r is the number of objects to be selected (in this case, the number of infielders needed).
Using this formula, we can calculate the number of ways to select 2 infielders from 4:
C(4, 2) = 4! / (2! * (4 - 2)! )
= 4! / (2! * 2!)
= (4 * 3 * 2!) / (2! * 2)
= (4 * 3) / 2
= 6
So, there are 6 ways to select 2 infielders from the 4 available infielders.
Next, let's calculate the number of ways to select 2 outfielders from the 6 available outfielders:
C(6, 2) = 6! / (2! * (6 - 2)! )
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / 2
= 15
There are 15 ways to select 2 outfielders from the 6 available outfielders.
To find the total number of ways to select 4 fielders (2 infielders + 2 outfielders), we multiply the number of ways to select 2 infielders by the number of ways to select 2 outfielders:
Total ways = 6 * 15
= 90
Therefore, there are 90 ways to send four fielders in a game consisting of 2 infielders and 2 outfielders.