Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 13 Aug 2015
Posts: 204
GPA: 3.82
WE: Corporate Finance (Retail Banking)

In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 05:24
Question Stats:
84% (01:17) correct 16% (01:29) wrong based on 147 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4551
Location: Canada

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
29 Aug 2018, 15:29
mkrishnabdrr wrote: 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 " ScienceScienceLab" This ensures that Science Lab immediately follows the Science class So, we now have only 4 classes: English, Math, History and ScienceScienceLabWe 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
_________________
Test confidently with gmatprepnow.com




Math Expert
Joined: 02 Sep 2009
Posts: 62352

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 05:30
mkrishnabdrr wrote: 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 Science, and Science Lab are fixed, so we have 4 units: {English}, {Math}, {History}, {Science, and Science Lab} The number of arrangements = 4! = 24. Answer: B.
_________________



Manager
Joined: 13 Aug 2015
Posts: 204
GPA: 3.82
WE: Corporate Finance (Retail Banking)

In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
Updated on: 04 Jul 2017, 05:39
Science cannot be placed in last slot because it must be followed by Science Lab. So, science has 4 possibilities. Science lab has to be placed immediately after science so it has 1 possibility. English 3, and Math 2. So, by fundamental counting principle, total ways=4 x 1 x 3 x 2=4 x6=24 Hence, B
Originally posted by mkrishnabdrr on 04 Jul 2017, 05:29.
Last edited by mkrishnabdrr on 04 Jul 2017, 05:39, edited 1 time in total.



Senior SC Moderator
Joined: 22 May 2016
Posts: 3667

In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 14:57
mkrishnabdrr wrote: 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 These arrangements are small enough that you could write them out. There's only one way to put SC and SL together in each arrangement; then multiply. SC  SL  3  2  1 = 6 3  SC  SL  2  1 = 6 3  2  SC  SL  1 = 6 3  2  1  SC  SL = 6 6 * 4 = 24 Answer B
_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date. Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has.  Margaret Mead



Manager
Joined: 28 Apr 2016
Posts: 81

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 20:51
mkrishnabdrr wrote: Science cannot be placed in last slot because it must be followed by Science Lab. So, science has 4 possibilities. Science lab has to be placed immediately after science so it has 1 possibility. English 3, and Math 2. So, by fundamental counting principle, total ways=4 x 1 x 3 x 2=4 x6=24 Hence, B Hi, IF the question said that 'the science and science lab class must always be together', then will the answer still remain the same?



Math Expert
Joined: 02 Sep 2009
Posts: 62352

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 21:05
ameyaprabhu wrote: mkrishnabdrr wrote: Science cannot be placed in last slot because it must be followed by Science Lab. So, science has 4 possibilities. Science lab has to be placed immediately after science so it has 1 possibility. English 3, and Math 2. So, by fundamental counting principle, total ways=4 x 1 x 3 x 2=4 x6=24 Hence, B Hi, IF the question said that 'the science and science lab class must always be together', then will the answer still remain the same? If it were: " in how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class or viseversa?", then the answer would be 4!*2, because Science, and Science Lab within their unit can be arranged in two ways: {Science, and Science Lab} and {Science Lab and Science}.
_________________



Manager
Joined: 28 Apr 2016
Posts: 81

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
04 Jul 2017, 21:50
Bunuel wrote: ameyaprabhu wrote: mkrishnabdrr wrote: Science cannot be placed in last slot because it must be followed by Science Lab. So, science has 4 possibilities. Science lab has to be placed immediately after science so it has 1 possibility. English 3, and Math 2. So, by fundamental counting principle, total ways=4 x 1 x 3 x 2=4 x6=24 Hence, B Thanks, that was my exact doubt.



Manager
Joined: 01 Nov 2017
Posts: 94
GMAT 1: 700 Q50 V35 GMAT 2: 640 Q49 V28 GMAT 3: 680 Q47 V36 GMAT 4: 700 Q50 V35
GPA: 3.84

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
19 Sep 2018, 02:53
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?
We have 5 items, E M H S L. We need to find how many unique orders can be created from those 5 items while having L following right after S. We GLUE S and L together as 1 item. Then we have only 4 items in total E M H SL.
Ways to organize E M H SL = 4! If the question says "Science and Science Lab must be adjacent to each other" then we will have to multiple 4! with 2 because S and L can switch places (therefore having a different order). In this question the positon of L is fixed after S. So we keep 4! as is. ANSWER IS 4!



Intern
Joined: 17 Feb 2020
Posts: 6

Re: In a certain summer school program, there are five periods in the day.
[#permalink]
Show Tags
17 Feb 2020, 22:16
English, Math, History, Science
4! = 24




Re: In a certain summer school program, there are five periods in the day.
[#permalink]
17 Feb 2020, 22:16






