Julia is casting a play with 4 main roles. Six students have tried out. How many different combinations of 4 students can Julia cast from the 6 students?
6C4 = 6C2 = 6*5 / 1*2 = 15
To find the number of different combinations of 4 students that Julia can cast from the 6 students, we can use the concept of combination.
The formula for combination is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of students (6 in this case), and r is the number of students to be selected (4 in this case).
Using this formula, we can calculate the number of different combinations as follows:
6C4 = 6! / (4!(6-4)!)
= 6! / (4!2!)
= (6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1 x 2 x 1)
= (720) / (48)
= 15
Therefore, Julia can cast the play from the 6 students in 15 different combinations of 4 students.
To find the number of different combinations of 4 students Julia can cast from the 6 students, we can use the concept of combinations.
The formula to calculate combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items (students in this case)
- r is the number of items to be chosen
In this case, n = 6 (total number of students) and r = 4 (number of roles to be filled).
Let's plug in the values into the combination formula and calculate the result:
C(6, 4) = 6! / (4!(6-4)!)
First, let's calculate the factorial of 6:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Next, let's calculate the factorial of 4:
4! = 4 * 3 * 2 * 1 = 24
Finally, let's calculate the factorial of (6-4):
2! = 2 * 1 = 2
Now, we can substitute these values into the combination formula:
C(6, 4) = 720 / (24 * 2)
= 720 / 48
= 15
Therefore, Julia can cast the play with 4 students in 15 different combinations.