Ben and Ann are among 7 contestants from which 4

Expert replies

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Dec 11, 2019 6:23 am

Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?

A. 5
B. 6
C. 7
D. 14
E. 21

OA A

Source: Official Guide

Like this post

Source: Beat The GMAT — Problem Solving | Wed Dec 11, 2019 6:23 am

GMAT/MBA Expert

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

by [email protected] » Wed Dec 11, 2019 9:09 pm

Hi All,

We're told that Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. We're asked of the different possible selections, how many contain NEITHER Ben nor Ann. Since we're selecting 'groups' of people, this is ultimately a Combination Formula question.

IF we had NO restrictions, then with 7 contestants, the number of 'groups of four' would be 7c4 = 7!/4!3! = (7)(6)(5)/(3)(2)(1) = 35 possible groups of four

However, we're interested in groups that contain NEITHER Ben nor Ann, which means that we have just 5 people to choose from. 5c4 = 5!/4!/1! = (5)/(1) = 5 groups of four.

Final Answer: A

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

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Thu Dec 12, 2019 5:45 am

BTGmoderatorDC wrote:Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?

A. 5
B. 6
C. 7
D. 14
E. 21

Let Ann, Bob, C, D, E, F, G be the 7 contestants.

To ensure that neither Ben nor Ann are among the four semifinalists, let's remove them from the list of contestants.

So, we can select the four semifinalists from {C, D, E, F, G}

Since the order in which we select the 4 semifinalists does not matter, we can use COMBINATIONS.
We can select 4 semifinalists from 5 contestants in 5C4 ways.
5C4 = 5

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Dec 12, 2019 6:34 pm

BTGmoderatorDC wrote:Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?

A. 5
B. 6
C. 7
D. 14
E. 21

OA A

Source: Official Guide

If neither Ben nor Ann is among the semifinalists, then there are only 5 contestants vying for the four slots. Thus, the number of ways to select the semifinalists when neither Ben nor Ann is selected is 5C4 = 5.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Thu Dec 19, 2019 9:40 pm

There are 7 contestants.
4 semi-finalists are to be selected.
Four different possible selection with neither Ann nor Bens
$$=\left(7-2\right)C_4$$
$$=5_{C_4}=\ \frac{5!}{4!}=\frac{5\cdot4!}{4!}=5$$
Answer = Option A

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review