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.
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 !) =