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
Mnenie [13.5K]
3 years ago
12

(a) There are $n$ chairs in a row. Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adj

acent.
(b) There are 10 chairs in a circle, labelled from 1 to 10. Find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent.


(c) There are $n$ chairs in a circle, labelled from 1 to $n.$ Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
Mathematics
1 answer:
elixir [45]3 years ago
8 0

Answer:

(A) P (n,k) = n!/(n-k)! divided by 2

(B) C (n,3) = n!/(12)(n-3)!

(C) C (n,k) = n!/(n-k)!(k!)

Step-by-step explanation:

Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.

We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.

For (B), n=10

C (n,3) = n!/(n-3)!(3!) divided by 2

3! = 3×2×1 = 6

The expression divided by 2 means it will be multiplied by 1/2

Hence 6×2 = 12

And we arrive at

C (n,3) =n!/(12)(n-3)!

You might be interested in
The figure below shows two half-circles at the ends of a rectangle with the dimension shown.
timurjin [86]

Answer:

D. 154

Step-by-step explanation:

The area of the rectangle is 15*5= 75 inches

The area of the 2 semicircles combined, which make a circle, are:

π*r², where r is 5

r²=25

π*25=78.53981633

75 + 78.53981633 is about 154

5 0
2 years ago
Two ships leave the same port at the same time. Two hours later ship A has traveled 12 miles and ship B has traveled 8 miles.
MakcuM [25]

Answer:

the angle between their paths is <em>100.8°</em>

Step-by-step explanation:

From the given information, you can construct a triangle, just like the one in the figure.

We will use the <em>Cosine Rule</em> which is:

c² = b² + a² - 2 b c cos(θ)

where

  • c = 16 miles
  • b = 8 miles
  • a = 12 miles

Therefore,

2 b c cos(θ) = b² + a² - c²

cos(θ) = (b² + a² - c²) / 2 b c

θ = cos⁻¹( (b² + a² - c²) / (2 b c) )

θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )

<em>θ = 100.8°</em>

<em></em>

Therefore, the angle between their paths is <em>100.8°</em>

4 0
3 years ago
What is the value of 6x2 when x = 1.5?<br><br> Round to the tenths place<br><br> pls help
Ivahew [28]

Answer:

13.5

Step-by-step explanation:

6 x^2

Let x= 1.5

6 ( 1.5) ^2

6 *2.25

13.5

5 0
3 years ago
Any number that can be written as a fraction is?
Roman55 [17]
Every whole number is a rational number because whole numbers can be written as fractions.
3 0
3 years ago
5y-10=-25<br><br> Whats the answer?
bagirrra123 [75]
Add 10
5y = -15
Y = -3
7 0
3 years ago
Read 2 more answers
Other questions:
  • A hot dog stand at the fair sells hot dogs for $2 and drinks for $1. If the number of hot dogs you bought is 8 less than four ti
    6·1 answer
  • Kenneth drove 174.2 miles in 3 7/20 hours. What was his average speed?
    14·1 answer
  • 2 to the power of 6 divided by 2?
    13·2 answers
  • Is there only one way to create a factor tree? Explain.
    10·1 answer
  • Find the measures of the numbered angles for each parallelogram number 11
    6·1 answer
  • Write each rational number in the form a/b where a and b are integers
    6·1 answer
  • Water hose has filled up 1/7 of a pool after 1/10 of an hour at this rate how many hours will it take to fill the pool
    13·2 answers
  • There are not asymptotes for the parent function<br> f (x) =1/x <br> True<br> False
    9·1 answer
  • Which of these lines have a scale factor of 2?
    8·2 answers
  • Kyle bought a DVD that cost $19.23, including tax. She gave the sales clerk a $20 bill. How much change should Kyle receive?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!