Question

How many ways are there for six dogs and four cats to sit in a row in a strawberry field so that no two cats sit next to each other? Each dog is distinct from other dogs and each cat is distinct from other cats.Hint: First position the dogs and then consider possible positions for the cats.

Answer 1

Answer: 5,760

Explanation:

`\\`It was given that each dog is distinct from other dogs and each cat is distinct from other cats, Also from the hint given, the First position is for the dogs.
`\\`Let D represent the dogs and C represent the Cat , then we have

`\\`D C D C D C D C D D or

`\\`D D C D C D C D C D or

`\\`D C DD C D C D C D or

`\\`D C D C D D C D C D or

`\\`D C D C D C DD C D

`\\`Each of the arrangements above could be done in

`\\`2 x 4! x 4! ( it is constant that D is starting , so I am only left with the arrangement of the remaining 5 D's , out of the remaining 5 D's it is also constant that tow of them will be together and this could be done in 2 ways, so I have 4! left for the D's and 4! also for the C's )

`\\`= 2 x 24 x 24

`\\` = 1 , 152

`\\`The total arrangement = 5 x 1 , 152

`\\`= 5,7 60 ways