Which inequality is true?

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

olya-2409 [2.1K]

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

8 0

3 years ago

The ratio of Kailyn's money to Nathan's money is 4:9. If Nathan has $45, how much do

natita [175]

Answer:

Step-by-step explanation:

Step one:

we are told that the ratio of Kailyn's money to Nathan's money is

4:9,

Nathan has $45, let Kailyn's money be x

therefore

4/9=x/45

cross multiply we have

9x=45*4

9x=180

divide both sides by 9

x=180/9

x=20

Kailyn's money is $20

Together they have =20+45= $65

6 0

3 years ago

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

hammer [34]

Do u still need help?

6 0

2 years ago

Read 2 more answers

Please help me i can give brainliest!

viva [34]

Answer:

skewed left

Step-by-step explanation:

8 0

3 years ago

The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line?

Tresset [83]

Answer:

(0, 22)

Step-by-step explanation:

So you have the equation:

$y-1=-7(x-3)$

So first let's define what the "y-intercept" is. The y-intercept, of a line is like the name implies, when the line intercepts or "passes" the y-axis. And if you were to take any point on the y-axis, the y-value may vary, but there is one value that doesn't change, and that's the x-value. the x-value is always going to be zero, no matter where you are on the y-axis. So to find the y-intercept simple plug 0 in as x. This gives you the equation:

$y-1 = -7(0-3)$

$y-1 = -7(-3)$

$y-1=21$

$y=22$

So the y-intercept is at (0, 22)

7 0

2 years ago