The method for calculating how many arrangements are feasible when only a few items are chosen from a collection of items that are unique is as follows:
[tex]^nC_k=\frac{n!}{k!(n-k)!}[/tex]
Where:
n – the sum of all the elements of a set
k – the number of selected objects (the order of the object may change)
! – factorial
For instance, 3!=1×2×3
So, according to the problem, there are [tex]^7C_3[/tex] possible groups of 3 women out of 7 women. And [tex]^5C_2[/tex] possible groups of 2 men out of 5 men.
Combining we get that there are [tex]^7C_3 ~^5C2[/tex] groups of 3 women and 2 men out of 7 women and 5 men.
Therefore, there are [tex]^7C_3 ~^5C2=\frac{7!}{3!4!}\frac{5!}{2!3!}= 350[/tex] possibilities.
Learn more about combinations here-
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