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It's a combination question I think 

Marika collects enamel pins. She is lining them up to display in her display case. Marika has 6 different floral pins, 4 different cartoon pins, and 3 different animal pins.

 

determine the number of ways in which all the pins can be lined up if the cartoon pins cannot be together.

 May 6, 2021
 #1
avatar+121055 
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The  total possible arrangements  =  ( 6  + 4  + 3)!  =  13 ! 

 

From this....we  want to subtract  all the arrangents where  the cartoon pins are  together

 

Note  that  the could occupy  (13 - 4  + 1)  = 10 positions  (positions 1 thru  10)

 

And for  each of  these  the other pins could be arranged  is  ( 6 + 3)!  = 9 !  ways

 

 

So....the  number of possible arrangements where  they  are  not together   =

 

13!  - 10 (9 !)    =  

 

6,223,392,000  ways

 

cool cool cool

 May 6, 2021

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