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I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

 Jun 22, 2024

Best Answer 

 #1
avatar+944 
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I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?   

 

Temporarily consider the group of three math books as one unit. 

 

Then, 1 group + 2 psych + 2 chem can arrange to 5P5 = 120 ways. 

 

But wait.  You could arrange the three math books 6 different ways. 

 

So all the possible arrangements is 120 • 6 = 720 ways.  

.

 Jun 22, 2024
 #1
avatar+944 
+1
Best Answer

 

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?   

 

Temporarily consider the group of three math books as one unit. 

 

Then, 1 group + 2 psych + 2 chem can arrange to 5P5 = 120 ways. 

 

But wait.  You could arrange the three math books 6 different ways. 

 

So all the possible arrangements is 120 • 6 = 720 ways.  

.

Bosco Jun 22, 2024

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