Question

14. In a production of Grease, eight actors are considered for the male roles of Danny, Kenickie, and Marty. In how many ways can the director cast the male roles? 15. Seven students have volunteered

Answer 1

The director can cast the three male roles in Grease in 336 different ways by using the permutation formula 8P3, which equals 8 x 7 x 6.

Step-by-step explanation:

To determine the number of ways the director can cast the male roles of Danny, Kenickie, and Marty from eight actors, we can use the concept of permutations since the order of selection matters. For the first role, Danny, there are 8 actors available. Once Danny has been cast, there are 7 actors left for the role of Kenickie. Similarly, after casting Kenickie, there are 6 actors left for the role of Marty. Thus, the number of possible ways to cast these three roles is a product of these choices, which can be calculated as 8 × 7 × 6.

Permutations of n distinct objects taken r at a time is given by the formula nPr = n! / (n - r)!. For these three roles, we have:
8P3 = 8! / (8 - 3)! = 8 × 7 × 6 = 336 possible ways to cast the actors.

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