A certain company has 18 equally qualified applicants for 4

BTGmoderatorLU wrote:Source: GMAT Prep

A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

A. 18
B. 72
C. 180
D. 1260
E. 3060

The OA is E

Since the order of the selected applicants does not matter, we can use combinations to solve this question.
We can select 4 applicants from 18 applicants in 18C4 ways.

I 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

Hi All,

We're told that a certain company has 18 equally qualified applicants for 4 open positions. We're asked for the number of different groups of 4 applicants that can be chosen by the company to fill the positions if the order of selection does not matter. This question is a fairly straight-forward Combination Formula question (Brent's solution shows how to work through that formula). Once you recognize that that formula can be applied, you can actually avoid doing some of that math though:

The numerator of that Combination Formula calculation will include the number 17. Since that number is a prime number, there's nothing in the denominator that can 'reduce it' - meaning that the correct answer MUST be a multiple of 17. As such, you can quickly eliminate the first 3 answers (since they are clearly NOT multiples of 17). With a little work, you can also eliminate Answer D (since it's not a multiple of 17 either). That just leaves the correct answer...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: GMAT Prep

A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

A. 18
B. 72
C. 180
D. 1260
E. 3060

The OA is E

Since order does not matter, 4 people can be chosen from 18 in:

18C4 = 18!/(4! x 14!) = (18 x 17 x 16 x 15)/4! = (18 x 17 x 16 x 15)/(4 x 3 x 2) = 3 x 17 x 4 x 15 = 3,060 ways.

Answer: E