smyarga wrote:
To answer the question we should know the total number of females and males available in the pool, n and m.
The solution for this is \(P_f^n*P_{50-f}^m\) if we consider all roles are different (otherwise \(C_f^n*C_{50-f}^m\)), where \(f\) is the total number of females.
Anyway, we have three unknown variables:\(n, m, f\)
(1) Insufficient. Give us only \(f=0.6*50\). We still don't know \(n, m\)
(2) Insufficient. \(P_{50-f}^m=116,280\). One equation in two variables and we still don't know \(n\).
(1)+(2). We can find \(m, f\), but we don't have any info about \(n\). Insufficient.
The answer is E.
What is the exact way to cast a play ?
Is it not number of ways to select men (for the roles) from among the total men available * number of ways to select females (for the roles) from the total number of females available?
if it could be explained in words please first, then in formula it would be easier to understand
I thought \(\hspace{8mm}C^{mr}_{males} * \hspace{8mm}C^{fr}_{females} \hspace{8mm}\) where \(mr\) is the number of male roles and \(fr\)is the number of female roles
Now assuming order is not important
(1)
60% of the acting pool is female: We get only males and females no information about how many male roles and how many female roles insufficient.
(2)
There are 116,280 ways to cast the male parts. No information about how many males or females or how many male roles or female roles
1+2
we can find total men and men roles , we can find total females but cannot get total female roles hence insufficient.
I hope my interpretation is correct for the total number of ways to cast a play, please do correct if it is wrong.
Thanks
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