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
den301095 [7]
3 years ago
14

DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be pl

ayed. Step 1 of 2 : If he has his choices narrowed down to 7 blues, 7 disco, 5 pop, and 7 reggae songs, and he wants to play no more than 4 reggae songs, how many different playlists are possible
Mathematics
1 answer:
Dominik [7]3 years ago
6 0

Answer:

Different playlists possible = 18287141644800

Step-by-step explanation:

Given - DJ Titus is making a playlist for a radio show; he is trying to

            decide what 10 songs to play and in what order they should be

            played.

            Step 1 of 2 : If he has his choices narrowed down to 7 blues,

                                 7 disco, 5 pop, and 7 reggae songs.

To find - He wants to play no more than 4 reggae songs.

              How many different playlists are possible ?

Proof -

Given that he wants to play no more that 4 reggae songs.

So the possibility of choice of reggae song is 0, 1, 2, 3, 4

Now,

Case I -

If 0 reggae song is selected

⇒All 10 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₁₀ ₓ ⁷C₀ = 92,378

Case II -

If 1 reggae song is selected

⇒All 9 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₉ ₓ ⁷C₁ = 646,646

Case III -

If 2 reggae song is selected

⇒All 8 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₈ ₓ ⁷C₂ = 1,587,222

Case IV -

If 3 reggae song is selected

⇒All 7 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₇ ₓ ⁷C₃ = 1,763,580

Case V -

If 4 reggae song is selected

⇒All 6 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₆ ₓ ⁷C₄ = 949,620

So,

Total possible ways = 92,378+ 646,646+ 1,587,222+ 1,763,580+ 949,620

                               = 5,039,446

⇒Total possible ways = 5,039,446

Now,

Also the 10 songs selected can arranged themselves in 10! ways. ( because order of song played does not matter )

∴ we get

Different playlists possible = 10! × 5,039,446

                                          = 18287141644800

⇒Different playlists possible = 18287141644800

You might be interested in
Would my answer choice be correct? ( There is a photo)
Leni [432]

Answer:

yes I believe so. best of luck

8 0
2 years ago
Three siblings- Kate, Sarah, and Dave- committed themselves to volunteer 160 hours for a homeless charity to build new housing .
liraira [26]

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

Step-by-step explanation:

Three siblings- Kate, Sarah, and Dave- committed themselves to

volunteer 160 hours for a homeless charity to build new housing

1. Dave worked 15 hours more than Kate

2. Sarah worked 5 hours fewer than Kate

3. The total hours for them is 160 hours

Assume that Kate worked for x hours

∵ Kate worked for x hours

∵ Dave worked 15 hours more than Kate

∴ Dave worked for x + 15 hours

∵ Sarah worked 5 hours fewer than Kate

∴ Sarah worked x - 5 hours

∵ They worked for 160 hours

- Add the number of worked hours of them and equate the sum

  by 160

∴ x + x + 15 + x - 5 = 160

- Add like terms in the left hand side

∴ 3x + 10 = 160

- Subtract 10 from both sides

∴ 3x = 150

- Divide both sides by 3

∴ x = 50 hours

∵ Kate worked for x hours

∴ Kate worked for 50 hours

∵ Dave worked for x + 15 hours

∴ Dave worked for 50 + 15 = 65 hours

∵ Sarah worked for x - 5 hours

∴ Sarah worked for 50 - 5 = 45 hours

Kate worked for 50 hours, Dave worked for 65 hours and Sarah

worked for 45 hours

Learn more:

You can learn more about equation in brainly.com/question/11229113

#LearnwithBrainly

6 0
3 years ago
(worth 100 points) Miguel is organizing his collection of sports memorabilia into glass display cases. He wants to cover each si
AlladinOne [14]

Answer:

4240 inches²

Step-by-step explanation:

In order to find the amount of film needed, we have to find the surface area of this cuboid.

  • Formula to Find Surface Area of Cuboid: 2(wl+hl+hw), where w = width, l = length, and h = height.

Now, let's solve!

  • 2(36*25+20*25+20*36)  
  • 2(900+500+720)
  • 2(2120)
  • 4240

Therefore, the answer is 4240 inches².

8 0
2 years ago
Read 2 more answers
C<br> 10 mm<br> 24 mm<br> What is the length of the hypotenuse?
kompoz [17]

Answer:

26

Step-by-step explanation:

The Pythagorean Theorem states that a² + b² = c²

so, c = √(a² + b²)

10² + 24² = 676

√676 = 26

5 0
2 years ago
Rectangle leg this 11feet and perimeter of 38feet what is the width of the rectangle in feet
jok3333 [9.3K]
2(11)+2x=38
22+2x=38
2x=38-22
2x=16
x=16/2
x=8
The width of the rectangle is 8 feet.
7 0
3 years ago
Other questions:
  • Thirty-five percent of what number is 10.5?
    7·2 answers
  • A ball has a diameter of 14 inches. Which choice is closest to its surface area? Use 3.14 to approximate pi.
    5·1 answer
  • "a survey of 700 non fatal accidents showed that 183 involved faulty equipment. find the point estimate for p, the population pr
    5·1 answer
  • Emily and Tammy each opened checking accounts on the same day, intending to withdraw money for weekly expenses. Emily opened her
    14·1 answer
  • What is 3 2/9 * -1 5/7
    10·1 answer
  • What is the area of a tank 42 meters tall and a diameter of 20 meters
    13·1 answer
  • A construction crew is paving a road. The crew has already paved 1,000 square feet and can pave at a rate of 300 square feet of
    8·1 answer
  • David is buying a cheese wheel priced at $14 before tax. The store charges 8%, percent sales tax
    7·1 answer
  • 3 3/16 divided 3/8?
    14·1 answer
  • How do you write 0.8 recurring as a fraction?<br><br>please can i have an explanation aswell :)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!