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
Artist 52 [7]
2 years ago
10

Twenty different books are to be put on five book shelves, each of which holds at least twenty books.

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
8 0

Answer:

(a) 10,626 different arrangements

(b) 95,367,431,640,625 different arrangements

(c) 2.5852017 × 10²² different arrangements

Step-by-step explanation:

(a) How many different arrangements are there if you only care about the number of books on the shelves (and not which book is where)?

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626 arrangements

(b) How many different arrangements are there if you care about which books are where, but the order of the books on the shelves doesn't matter?

Since the order of the books on the shelves does not matter,

The calculation is given as

5²⁰ = 95,367,431,640,625 arrangements

(c) How many different arrangements are there if the order on the shelves does matter?

Since order matters now

Step 1

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626

Step 2

We find the factorial of the number books

= 20!

= 2,432,902,008,176,640,000

Step 3

The different arrangements there are if the order on the shelves does matter is calculated

= 10,626 × 2,432,902,008,176,640,000

= 2.5852017 × 10²² different arrangements

You might be interested in
What is the measure of angle X
algol [13]

Answer:

30 degrees ???

Step-by-step explanation:

3 0
2 years ago
A football team scored 3 touchdowns, 3 extra
Reil [10]

Answer:

3x6+3x1+4x3

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Can 1 be expressed as a fraction
elixir [45]

  • <em><u>Any integer can be written as a fraction! Just put that integer as the numerator of a fraction with a denominator of 1.</u></em>

<h2><em><u>hope</u></em><em><u> it</u></em><em><u> helps</u></em><em><u>!</u></em></h2><h2><em><u>#</u></em><em><u>c</u></em><em><u>a</u></em><em><u>r</u></em><em><u>r</u></em><em><u>y</u></em><em><u> </u></em><em><u>on </u></em><em><u>learning</u></em></h2>

6 0
2 years ago
Read 2 more answers
I need help in part b.please help : )
Salsk061 [2.6K]
1,534 divided by 26 equals 59
Hope this helps !!!
7 0
3 years ago
The proceeds from a car wash are directly proportional to the number of cars washed. The total after 9 cars was $180. How much c
Westkost [7]

Answer:

$1200

Step-by-step explanation:

180 divided by 9 is 20, so they earned $20 per car washed. They want to wash 60 cars, and if they wash 60 cars they would earn $1200. (60 x 20)

5 0
3 years ago
Read 2 more answers
Other questions:
  • 1. Which of the following terms describes a figure that extends continuously in two directions?
    12·2 answers
  • Use complete sentences to describe why the product of x3 and x7 is x10.
    8·1 answer
  • Two classmates are preparing research papers and are organizing their information on index cards.
    10·1 answer
  • Solve the equation 5a+5=30
    5·2 answers
  • Is y=-1/3x parallel or perpendicular
    7·1 answer
  • I need help ASAP!!! Please explain how to solve the problem
    5·1 answer
  • the width of a rectangle is 2 more than 4 times its length. The perimeter of the rectangle is 24 centimeters. Find the width of
    13·1 answer
  • 10×3×4×4×4×4×4÷2 answer pls​
    10·2 answers
  • The sales tax for an item was $19.50 and it cost $390 before tax.
    11·1 answer
  • Identify an equation in point-slope form for the line perpendicular to y = -1/2x + 11 that passes through (4, -8)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!