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
vodka [1.7K]
3 years ago
6

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. There is someone with a very bad

cough who must sit at least one seat away from anyone else. How many ways can this happen?
Mathematics
1 answer:
diamong [38]3 years ago
5 0

Answer: 12,972,960

Step-by-step explanation: There are 14 chairs and  8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆  x 3! 

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways

The 2nd has a choice among 13 ways

The 3rd has a choice among 12 ways

The 4th has a choice among 11 ways

The 5th has a choice among 10 ways

The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways

But the 3 (that formed one group) could seat among themselves in 3!

or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

You might be interested in
What number is 100,000 more than 75,000 and explain how u got answer
alina1380 [7]
100,000 + 75,000 = 175,000. To get the answer, you add the two.
6 0
3 years ago
Write an expression to represent the perimeter of:<br> 2a-3<br> 2a<br> 3a+1
Marina86 [1]
I am assuming this is a triangle.....P = a + b + c

P = 2a - 3 + 2a + 3a + 1....combine like terms
P = 7a - 2 <==
5 0
3 years ago
Help me!! answer all ​
Sergio [31]

its blurry

Step-by-step explanation:

can you take a better picture

3 0
2 years ago
Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative
Jet001 [13]

The ordered pair that represents a function is:

⇒ (-3, 3), (-2, -2), (1, 1), (2, -2)

<u>What are Coordinates?</u>

A pair of numbers that describe the exact position of a point on a cartesian plane by using horizontal and vertical lines are called the coordinates.

The given points are;

(-3, 3), (-3, -3), (-1, 1), (1, 4)

(-3, 3), (-2, -2), (1, 1), (2, -2)

(-3, 3), (-3, -3), (1, -4), (1, 1)

(-4, 4), (-4, 1), (-2, 1), (2, 1)

Now, For an ordered pair to be a function, either of the following must be true:

Each x-value has exactly one corresponding y-value.

More than one x-values have the same corresponding y-values.

And, If any of the following conditions is true, then the ordered pair is not a function,

One x-value has multiple corresponding y-values.

More than one x-values have multiple corresponding y-values.

From the given options, only ordered pair  (-3, 3), (-2, -2), (1, 1), (2, -2) satisfies the condition to be a function.

Because none of its x-values have multiple corresponding y-values.

And, Other ordered pairs are either one-to-many or many-to-many.

So, The ordered pair that represents a function is:

⇒  (-3, 3), (-2, -2), (1, 1), (2, -2)

To learn more about ordered pairs visit:

brainly.com/question/19267542

#SPJ1

4 0
1 year ago
B = 54°, b=15, c=<br> c = ? (Round answers to<br> the nearest hundredth.)
zaharov [31]

Answer:

18.54

Step-by-step explanation:

sine is opposite/hypotenuse, and you have opposite (b=15), so use that

sin(54) = 15/c

c = 15/sin54

then use calculator

c = 18.54

8 0
2 years ago
Other questions:
  • How many eights are there in 4 1/4
    11·2 answers
  • Please solve much appreciated!
    8·2 answers
  • I need to know why the answer is 12.5 and how you got it.
    6·1 answer
  • Lacy runs 5 1/4 km on Thursday. She runs 1 1/2 times as far on Saturday. How far does Lacy run on Saturday? Express your answer
    13·1 answer
  • Simplify the fractions
    14·2 answers
  • Find the indicated limit. ModifyingBelow lim With x right arrow 8 StartRoot 7 x minus 2 EndRoot Select the correct choice below
    15·1 answer
  • Okay so i'm confused about this question. Write an inequality for the phrase ''two more than three times a number is at most 53.
    14·1 answer
  • The confidence interval based on the two-sample design is wider because there is considerable variation in mileage between the c
    11·1 answer
  • Find the area of the circle. (Take pi 22/7
    9·1 answer
  • PLEASE HELP !!!!! 2 - 19 = 2?<br> BTW BTS OUTSOLD AND PAVED THE WAY !!!!!!!!!!
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!