Mathematics, 01.07.2019 18:40 NaVaThEBeAsT

There are 17 portable mini suites (a. k.a. cages) in a row at the paws and claws holiday pet resort. they are neatly labeled with their guests' names. there are 8 poodles and 9 tabbies. how many ways can the "suites" be arranged if:

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Answer from: googoo4

Given that there are 17 portable mini suites (a.k.a. cages) in a row at the Paws and Claws Holiday Pet Resort. They are neatly labeled with their guests' names. There are 8 poodles and 9 tabbies. How many ways can the "suites" be arranged if: a) there are no restrictions.

b) cats and dogs must alternate.

c) dogs must be next to each other.

d) dogs must be next to each other and cats must be next to each other.

Part A:

If there are no restrictions, then the number of ways the "suites" can be arranged is given by:

$17!=17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1=355,687,428,096,000 \ ways$

Part B:

If cats and dogs must alternate, then the number of ways the "suites" can be arranged is given by:

$9!\times8!=9\times8\times7\times6\times5\times4\times3\times2\times1\times8\times7\times6\times5\times4\times3\times2\times1=14,631,321,600 \ ways$

Part C:

If dogs must be next to each other, then the group of dogs are taken as 1 object and there are now 10 objects to arrange. The number of ways to arrange 10 objects is given by:

$10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3,628,800
 \ ways$

Also, the group of dogs can be arranged in:

$8!=8\times7\times6\times5\times4\times3\times2\times1=40,320
 \ ways$

Therefore, the total number of ways the "suites" can be arranged is given by:

$10!\times8!=3,628,800\times40,320=146,313,216,000 \ ways$

Part D:

If dogs must be next to each other and cats must be next to each other, then the group of dogs are taken as 1 object and the group of cats are taken as 1 object, then there are now 2 objects to arrange.

The number of ways to arrange two objects is given by:

$2!=2\times1=2$

The number of ways the 9 dogs are to be arranged is given by:

$9!=9\times8\times7\times6\times5\times4\times3\times2\times1=362,880$

The number of ways the 8 cats are to be arranged is given by:
$8!=8\times7\times6\times5\times4\times3\times2\times1=40,320$

Therefore, the total number of ways the "suites" can be arranged is given by:

$2!\times9!\times8!=2\times362,880\times40,320=29,262,643,200 \ ways$

Answer from: Quest

i got 142 as my answer

step-by-step explanation:

Answer fast and i’ll give you brainliest

Answer from: Quest

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

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There are 17 portable mini suites (a. k.a. cages) in a row at the paws and claws holiday pet resort....