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

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Re: In a certain summer school program, there are five periods in the day. [#permalink]
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mkrishnabdrr
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]
mkrishnabdrr
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]
mkrishnabdrr
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]
ameyaprabhu
mkrishnabdrr
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]
Bunuel
ameyaprabhu
mkrishnabdrr
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]
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]
English, Math, History, Science

4! = 24
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Re: In a certain summer school program, there are five periods in the day. [#permalink]
mkrishnabdrr
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
Solution:

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.

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

We have 4 options available
1. English
2. Math
3. History
4. Science and science lab

Number of ways to arrange the 4 options = 4! = 24

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