This is a permutation problem because the order in which the actors are selected matters (i.e., being chosen as Larry is different from being chosen as Curly or Moe).

Step 1: Determine the total number of actors. In this case, there are 8 actors.

Step 2: Determine the number of roles to be filled. In this case, there are 3 roles (Larry, Curly, and Moe).

Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of options, r is the number of selections to be made, and "!" denotes factorial (the product of an integer and all the integers below it, e.g. 4! = 4*3*2*1 = 24).

Step 4: Substitute the given values into the formula. So, we have 8P3 = 8! / (8 - 3)!

Step 5: Simplify the equation. 8P3 = 8! / 5! = (8*7*6*5*4*3*2*1) / (5*4*3*2*1) = 8*7*6 = 336.

So, there are 336 different ways the roles could be cast.

Question

This is a permutation problem because the order in which the actors are selected matters (i.e., being chosen as Larry is different from being chosen as Curly or Moe).

Step 1: Determine the total number of actors. In this case, there are 8 actors.

Step 2: Determine the number of roles to be filled. In this case, there are 3 roles (Larry, Curly, and Moe).

Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of options, r is the number of selections to be made, and "!" denotes factorial (the product of an integer and all the integers below it, e.g. 4! = 4*3*2*1 = 24).

Step 4: Substitute the given values into the formula. So, we have 8P3 = 8! / (8 - 3)!

Step 5: Simplify the equation. 8P3 = 8! / 5! = (8*7*6*5*4*3*2*1) / (5*4*3*2*1) = 8*7*6 = 336.

So, there are 336 different ways the roles could be cast.

Knowee AI · Accepted Answer

This is a permutation problem because the order in which the actors are selected matters (i.e., being chosen as Larry is different from being chosen as Curly or Moe).

Step 1: Determine the total number of actors. In this case, there are 8 actors.

Step 2: Determine the number of roles to be filled. In this case, there are 3 roles (Larry, Curly, and Moe).

Step 3: Use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of options, r is the number of selections to be made, and "!" denotes factorial (the product of an integer and all the integers below it, e.g. 4! = 4*3*2*1 = 24).

Step 4: Substitute the given values into the formula. So, we have 8P3 = 8! / (8 - 3)!

Step 5: Simplify the equation. 8P3 = 8! / 5! = (8*7*6*5*4*3*2*1) / (5*4*3*2*1) = 8*7*6 = 336.

So, there are 336 different ways the roles could be cast.

There are 8 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?

Question

There are 8 different actors auditioning for the roles of Larry, Curly and Moe. How many ways could the roles be cast?

Solution

Similar Questions

Upgrade your grade with Knowee