Question

In a production of Grease, eight actors are considered for the male roles of Danny, Kenickle, and Marty. In how many ways can the director cast the male roles?

A. 24

B. 336

C. 512

D. 1,024

Answer 1

The director can cast the male roles in Grease in 336 different ways using the concept of permutations.

Step-by-step explanation:

To find the number of ways the director can cast the male roles in Grease, we can use the concept of permutations. Since there are 8 actors considered for the 3 male roles, we need to calculate 8P3, which represents selecting 3 actors from a pool of 8 without replacement, and the order of selection matters. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items being selected.

Using the formula, we can calculate:

1. 
   
3. 8P3 = 8! / (8 - 3)! = 8! / 5! = (8 * 7 * 6 * 5!) / 5! = 8 * 7 * 6 = 336

Therefore, the director can cast the male roles in Grease in 336 different ways.