In a certain summer school program, there are five periods

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Wed Aug 29, 2018 2:56 pm

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Source: Magoosh

In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

A. 20
B. 24
C. 100
D. 120
E. 135

The OA is B.

Source: Beat The GMAT — Problem Solving | Wed Aug 29, 2018 2:56 pm

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In a certain summer school program, there are five periods

by Brent@GMATPrepNow » Wed Aug 29, 2018 3:30 pm

BTGmoderatorLU wrote:Source: Magoosh

In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

A. 20
B. 24
C. 100
D. 120
E. 135

Take the Science, and Science Lab classes and "glue" them together to get the super class "Science-Science-Lab"
This ensures that Science Lab immediately follows the Science class

So, we now have only 4 classes: English, Math, History and Science-Science-Lab
We can arrange n objects in n! ways.
So, we can arrange these 4 classes in 4! ways (i.e. 24 ways)

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Aug 29, 2018 7:33 pm

BTGmoderatorLU wrote:Source: Magoosh

In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

A. 20
B. 24
C. 100
D. 120
E. 135

Alternate approach:

Since Science class must be followed immediately by Science lab, Science class cannot be taken during the last period.
Thus:
Number of options for Science class = 4. (Any of the first 4 periods.)
Number of options for Science lab = 1. (Must be the period immediately after Science class.)
Number of ways to arrange the remaining 3 classes = 3! = 6.
To combine the options above, we multiply:
4*1*6 = 24.

The correct answer is B.

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by Jeff@TargetTestPrep » Wed Sep 05, 2018 9:38 am

BTGmoderatorLU wrote:Source: Magoosh

In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

A. 20
B. 24
C. 100
D. 120
E. 135

We can group Science and Science Lab together as one class, so there are actually 4 classes to be arranged; the number of ways to arrange them is 4! = 24.

Answer: B

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