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# In a certain summer school program, there are five periods in the day.

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In a certain summer school program, there are five periods in the day.  [#permalink]

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04 Jul 2017, 05:24
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Question Stats:

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

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29 Aug 2018, 15:29
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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 "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)

Cheers,
Brent
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Re: In a certain summer school program, there are five periods in the day.  [#permalink]

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04 Jul 2017, 05:30
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1
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.

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In a certain summer school program, there are five periods in the day.  [#permalink]

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Updated on: 04 Jul 2017, 05:39
1
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.
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In a certain summer school program, there are five periods in the day.  [#permalink]

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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

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

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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?
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Re: In a certain summer school program, there are five periods in the day.  [#permalink]

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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 vise-versa?", 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}.
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Re: In a certain summer school program, there are five periods in the day.  [#permalink]

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

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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!
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Re: In a certain summer school program, there are five periods in the day.  [#permalink]

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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
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