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 ot

Question

2 years ago

9

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 ot

her? 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.

Mathematics

1 answer:

pickupchik [31] · Answer 1 · 2022-05-13T10:25:59+03:00

Answer: 5,760

Step-by-step 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