Question

You are trying to cast four roles for a play. 12 actors try out, including sir Ian McKellen and Patrick Stewart. the director tells you that in order to bring the crowds, you must include at least one of sir Ian and Patrick in the cast. How many casts are possible?

Answer 1

Answer:

6,840 casts

Step-by-step explanation:

Assuming that every actor can play each of the 4 roles and that each role is different, the number of possible casts including at least one of sir Ian and Patrick is given by the total number of possible casts (permutation of 4 out of 12 actors), minus the number of casts without sir Ian and Patrick (permutation of 4 out of 10 actors):

$n=\frac{12!}{(12-4!)} -\frac{10!}{(10-4)!}\\n=(12*11*10*9)-(10*9*8*7)\\n=6,840\ casts$

There are 6,840 possible casts.