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
Please help!! This is for a test!!
masya89 [10]
Cos=(adjacent/hypotenuse)
So the answer will be cos(16/20) or cos(4/5) both will give u the same answer
I hope it helps
6 0
3 years ago
6p+2+ p - 3 = 8p - 8​
saul85 [17]
6p+p+2-3=8p-8
7p-1=8p-8
1=1p-8
7=1p
p=7
7 0
3 years ago
Three consecutive numbers are such that when they are taken in increasing order and multiplied by 2,3and 4 respectively, they ad
Ivenika [448]

Answer:

7 , 8 , 9

Step-by-step explanation:

Assume three consecutive number are,

x , (x+1) , (x+2)

Multiplied by 2 ,3 and 4 respectively

2x , 3(x + 1) , 4(x + 2)

Sum of all = 74

So,

2x + 3(x + 1) + 4(x + 2) = 74

2x + 3x + 3 + 4x + 8 = 74

9x + 11 = 74

9x = 63

x = 7

So,

x , (x+1) , (x+2)

7 , (7+1) , (7+2)

7 , 8 , 9

3 0
3 years ago
The sum of the interior angles S of a polygon with n sides is given by the formula S = 180(n-2).
shusha [124]

Answer:

,

Step-by-step explanation:

4 0
3 years ago
Can you help me with this like explain how and stuff, Please?
eduard

Answer:

Step-by-step explanation:I belive that the 7x+22 needs to equal 50 because they opposite angles. Hope this helped a little and can get you started

7 0
3 years ago
Read 2 more answers
Other questions:
  • On a map the key indicates that one inch equals 50 miles. It is 600 miles from Ricky's house to the Willis tower in Chicago. Wha
    12·1 answer
  • Please help, and show work, I need to understand. Thank you
    6·1 answer
  • A car is designed to last an average of 12 years with a standard deviation of 0.8 years. What is the probability that a car will
    10·1 answer
  • Write the function shown on the graph
    13·1 answer
  • A catering company loses $110 as a result of a delay.
    9·1 answer
  • Which property is used in the following expression ? 8(2 + 7) = 16 + 56
    9·2 answers
  • Please help will give brainliest
    15·1 answer
  • £50 is divided between Krutika, Natasha & Richard so that Krutika gets twice as much as Natasha, and Natasha gets three time
    11·2 answers
  • Which function is the inverse of a quadratic function?
    11·1 answer
  • a shipping box has the dimensions of 12inches, 16 inches, and 24 inches. what is the length of the longest item that could fit i
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!