Nine actors audition for four different parts in a play.
In how many ways can the play director fill these roles?
A) 368,880
B) 15,120
C) 3024
D) 126
What is your choice and why ?
C
9P4 = C
There are 9 slots, in which 4 parts can be placed in. Order also matters for each part/role. Therefore, 9P4
To calculate the number of ways the play director can fill these roles, we need to use the concept of combinations.
For the first role, the director can choose one actor from the nine available. This leaves eight actors for the second role. For the third role, there are seven actors left to choose from, and for the fourth role, six actors are available.
To calculate the total number of ways, we multiply these individual choices together:
9 * 8 * 7 * 6 = 3,024
Therefore, the correct answer is C) 3024.
To solve this problem, we can use the concept of permutations. Permutations are arrangements of objects in a specific order.
In this case, we have nine actors auditioning for four different parts in the play. This means that we need to find the number of ways the director can assign actors to these four roles.
In the first role, the director can choose any of the nine actors. For the second role, since one actor has already been assigned, there are only eight remaining actors to choose from. For the third role, there are seven remaining actors, and for the fourth role, there are six remaining actors.
To find the total number of ways, we multiply the number of choices for each role:
9 * 8 * 7 * 6 = 3,024
Therefore, the answer is C) 3,024.