1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Degger [83]
3 years ago
8

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:
Mathematics
1 answer:
DiKsa [7]3 years ago
4 0
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
You might be interested in
Below are two linear equations . 1: y - 2 = 4/5 * (x + 4) 2: 5x + 4y = - 20 a) Are the lines 1 and 2 parallel , perpendicular or
Olenka [21]
Perpendicular and 2 I think that’s right
5 0
3 years ago
1
Sauron [17]

Answer:

Step-by-step explanation:

"Four times a number" in symbols is "4n."

6 0
3 years ago
Pam’s grandfather has a garden that measures 4 feet by 6 feet. How much will the area be increased if he doubles the length and
ExtremeBDS [4]

Answer:

The area will be increased by 72 feet.

Step-by-step explanation:

4 x 6 = 24

Now we have to double those lengths.

We know that 4 x 2 is 8 and 6 x 2 is 12.

So the new equation would be: 8 x 12 = 96

Now we take the original area and subtract it by the new area.

96 - 24 = 72

Hope this helps:)

7 0
2 years ago
Suppose the diameter of a circle is 16. What is its radius?
Rashid [163]
The radius is 8 because its half the diameter.
6 0
3 years ago
Read 2 more answers
Y=-3x+9<br> y=-x-5 <br><br> what is the solution for the system of equations?
alexandr402 [8]

Our system of equations is:

y = -3x + 9

y = -x - 5


To solve this system of equations, we are going to use substitution. This means that we are going to substitute the second equation into the first equation since both are already solved for y in terms of x.


y = -3x + 9

-x - 5 = -3x + 9


Now, we must simplify by moving all of the constant terms to one side of the equation and all of the variable terms to the other side.


-x - 5 = -3x + 9

2x - 5 = 9

2x = 14


Finally, to undo the multiplication between the coefficient 2 and the variable x, we must divide both sides by 2 to get the variable x alone.


x = 7


Next, we must substitute in this value we have solved for x into one of the original equations to solve for the other variable, y.


y = -3x + 9

y = -3(7) + 9


To simplify, we must multiply through the parentheses and combine like terms by addition.


y = -21 + 9

y = -12


Therefore, your final answer is x = 7 and y = -12, or as an ordered pair (7, -12).


Hope this helps!

6 0
3 years ago
Other questions:
  • Estimate the quotient 8 1/6 / 1 7/8
    12·1 answer
  • PLEASE HELP IM DYING AND DUMB
    13·2 answers
  • Solve 27 and 29, will give BRAINLIST!!
    13·2 answers
  • Emma decides to invest $990,000 in a period annuity that earns a 2.2% APR,
    12·2 answers
  • Which is equivalent to 5 Square root of 1215^x
    6·2 answers
  • Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5
    6·1 answer
  • The sides of a rectangular room are perpendicular to each other.
    10·1 answer
  • 1) A builder laying the foundations of a garage wants to be sure he has the walls of the garage are at right angles. The length
    12·1 answer
  • 5.2% of 628.55km rounded to two decimal places​
    11·1 answer
  • ​Mr. Allen says that the equation y=2x+1 has a solution of (4, 9). Is Mr. Allen right or wrong?​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!