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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?

 Oct 17, 2024
 #2
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= 7! / (3! * 2! * 2!) = 5040/(6 * 2 * 2) = 5040/24 = 210 ways

 Oct 17, 2024
 #3
avatar+37147 
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Oopps...I didn't read the entire question ...

  the three math books together can be arranged in   6 ways    ( 3!   or  3 P3) 

   then they act as one object of 5 objects     5 P 5 = 120 ways to arrange the books     ( 5!) 

 

Then  6 x 120 =   720 ways    

 Oct 17, 2024

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