A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by company to fill the positions if the order of selection doesn't matter?
18
72
180
1260
3060
Permutaion and combination
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Since the order of the selected applicants does not matter, we can use combinations to solve this question.josh80 wrote:A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by company to fill the positions if the order of selection doesn't matter?
A) 18
B) 72
C) 180
D) 1260
E) 3060
We can select 4 applicants from 18 applicants in 18C4 ways.
We have a free video on calculating combinations in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
In this video, we learn how to first take a combination like 18C4 and rewrite it as ...
(18)(17)(16)(15)/(4)(3)(2)(1) We now need to EVALUATE this.
First recognize that we can simplify some parts to get: (18)(17)(2)(5)
IMPORTANT: Since the answer choices are so SPREAD APART, we can likely use some estimation, rather than evaluate (18)(17)(2)(5)
First notice that, (18)(17)(2)(5) = (18)(170)
Now notice that (10)(170) = 1700, which means (18)(170) must be GREATER than 1700
So, the correct answer must be greater than 1700
Choose E
Cheers,
Brent