A certain company has 18 equally qualified applicants for 4

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A certain company has 18 equally qualified applicants for 4

by BTGmoderatorLU » Sat Nov 16, 2019 3:28 am

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

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Source: Beat The GMAT — Problem Solving | Sat Nov 16, 2019 3:28 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Nov 16, 2019 6:15 am

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

Brent Hanneson - Creator of GMATPrepNow.com

Quote

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Nov 16, 2019 10:19 am

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

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 22, 2019 11:22 am

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]