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avatar+1748 

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all the psychology textbooks are together?

 May 23, 2024
 #1
avatar+810 
0

First, let's see how many ways there are to arrange the 3 psychology books. 

 

We have 4p3 ways the arrange the books multiplied by the number of ways to put these books into the group of 7, which is 4. 

 

We have 24*4 = 96. 

 

Now, there are 4p4 ways to arrange the math books, which is simply 24. 

 

96*24 = 2304. 

 

There are 2304 ways to arrange the books! 

 

Thanks! :)

 May 23, 2024
 #2
avatar+129505 
+1

The psychology textbooks can be grouped together in one of  five positions....and  for each of these, they can be arranged 3!  = 6 ways

 

And for each of  the above arrangements the math textbooks can be  arranged in 4! = 24 ways

 

So

 

5 * 3! * 4!   =

 

5 * 6 * 24  =

 

720 ways

 

cool cool cool

 May 24, 2024

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