7 girls audition for 12 roles in a school play. What is the probability that at least 2 of the girls audition for the same part?

I am wondering if girls will be assigned multiple parts in the play, and do they know that...seven girls for 12 parts...

Keep in mind....its algebra. :)

To determine the probability that at least 2 girls audition for the same part, we can use the concept of complement probability.

First, let's calculate the probability that no two girls audition for the same part.

The first girl can choose any of the 12 roles. The second girl can choose from the remaining 11 roles since she cannot choose the same part as the first girl. The third girl can choose from the remaining 10 roles, and so on.

Therefore, the probability that no two girls audition for the same role is:
(12/12) * (11/12) * (10/12) * (9/12) * (8/12) * (7/12) * (6/12) * (5/12) * (4/12) * (3/12) * (2/12) * (1/12)

Next, we can find the probability that at least 2 girls audition for the same role by subtracting the probability of none of them auditioning for the same role from 1.

Probability of at least 2 girls auditioning for the same part = 1 - Probability of no two girls auditioning for the same part

Therefore, the probability that at least 2 girls audition for the same part can be calculated by substituting the above values into the formula:

Probability of at least 2 girls auditioning for the same part = 1 - [(12/12) * (11/12) * (10/12) * (9/12) * (8/12) * (7/12) * (6/12) * (5/12) * (4/12) * (3/12) * (2/12) * (1/12)]

Calculating this expression will give you the desired probability.