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1. A teacher arranged her books on a shelf. She has 4 astronomy books, 3 Biology books, and 2 Chemistry books. How many ways can she arrange these books on the shelf if the books from each subject must be together?

 

2. How many ways can David, Sam, Emma, and Lanie stand in a line if David and Sam refuse to stand next to each other?

 Jun 2, 2021
 #1
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1. A teacher arranged her books on a shelf. She has 4 astronomy books, 3 Biology books, and 2 Chemistry books. How many ways can she arrange these books on the shelf if the books from each subject must be together?

 

The  number of ways  =    arrangements in each topic * arrangements of topics =   4!  * 3!  * 2!  *  3!  = 

 

1728  arrangements

 

 

2. How many ways can David, Sam, Emma, and Lanie stand in a line if David and Sam refuse to stand next to each other?

 

 

Number of   ways  without restrictions  =  4!  =   24

 

Number  of ways  if David and Sam DO  stand next to each other   =  3 places they can occupy * 2 arrangements in each place   =   6

 

So.....number of  ways  if  they refuse to stand next to each other  =  24  -  6   =   18 ways

 

 

 

 

cool cool cool

 Jun 2, 2021

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