25. Julia is casting a play with 3 lead roles. Five students have tried out for each part. As long as no students have tried out for more than one part, how many different ways can Julia cast the lead roles?
A.60
B.80
C.125
D.25
E.50
5*5*5 = 125
she has 5 choices for each part.
Well, Julia's got quite the task ahead of her. With 3 lead roles and 5 students trying out for each part, she's going to have to make some tough choices.
Now, keep in mind that no student can try out for more than one part. So for the first lead role, Julia has 5 options to choose from. Once she's made that tough decision, she's left with 4 students to choose from for the second lead role. And for the final lead role, she's got 3 students left to consider.
To find out how many different ways Julia can cast the lead roles, we simply multiply the number of options for each role together: 5 x 4 x 3 = 60.
So, the answer is A.60. Julia has 60 different ways she can cast the lead roles. Let's wish her luck, because she's got some difficult decisions to make!
To solve this problem, we need to calculate the number of ways Julia can cast the lead roles without any student trying out for more than one part.
For the first lead role, she can choose any of the 5 students who tried out for that part. This gives us 5 possibilities.
For the second lead role, she can choose any of the remaining 4 students who have not yet been cast in any role. This gives us 4 possibilities.
Finally, for the third lead role, she can choose any of the remaining 3 students who have not yet been cast in any role. This gives us 3 possibilities.
Therefore, the total number of different ways Julia can cast the lead roles is given by:
5 * 4 * 3 = 60
So, the correct answer is option A. 60.
To find the total number of different ways Julia can cast the lead roles, we need to multiply the number of choices she has for each role. Since there are 3 lead roles, we need to find the number of choices for each role and then multiply them together.
For the first role, Julia has 5 students to choose from. Once she selects a student for the first role, there are 4 students left for the second role. Similarly, after selecting two students, there are 3 students left for the third role.
Therefore, the number of ways Julia can cast the lead roles is: 5 choices for the first role × 4 choices for the second role × 3 choices for the third role = 5 × 4 × 3 = 60.
Therefore, the correct answer is A. 60.