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.

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

answer is 144

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet