Probability #2

Total no. of ways 3 roles can be given to 5 actresses = 5C3 = 10

Since, Julia and Hallie have to be there in the film, this leaves only 1 role.This can be given to any remaining 3 actresses in 3 ways.

Thus, P = 3/10

C wrote:Five A-list actresses are vying for the three leading roles in the film, "Catfight in Denmark." The actresses are Julia Robards, Meryl Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actress has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

OA is [spoiler]3/10[/spoiler].

Source is MGMAT Word Translations, no answer choices given. I did not understand the explanation. Can someone please solve and explain?

Thanks.

First round of selection, the probability of selecting either either Julia or Hallie is 1/5 * 3 = 3/5 (Suppose only one actress is needed, the probability is 1/5, however, now 3 will be selected out of 5. So times 3.)

Second round of selection, the probability of selecting the remaining one of the pair, should be simplified as selecting two actresses out of 4, the probability is 1/4*2 = 1/2.

So the probability that Julia and Hallie will star together is 3/5 * 1/2 = 3/10.

Hi,

My approach to solve to this problem would:

p= Favorable ways /Total number of ways

Favourable ways:
There are 5 actresses ,Julia and Hallie must be there so we are left with picking one actress out of the remaining 3.
Total number of ways to choose 1 actress out of 3 would be 3C1.
Do remember there is only one way to choose Julia and Hallie 1C1 * 1C1.

Favorable ways = 1C1 * 1C1 * 3C1 = 3

Total number of ways:

Choose any 3 actresses randomly from the given 5 choices.
Number of ways = 5C3 = 10


p= Favorable ways /Total number of ways = 3/10.