One Direction Soundtrack lists

Edit: Kelvin did this not me!!

Combinations

Cynthia is a huge fan of One Direction. However, she doesn’t own one of their albums. So she decides to create her own album with their songs. Since Cynthia doesn’t know how to burn a CD, she gets Kelvin to help her burn it. Kelvin hates One Direction and doesn’t know what songs she likes except for One Thing, What Makes You Beautiful and Live While We’re Young. One Direction has a total of 20 songs. But an average CD can only hold up to 15 songs. Kelvin decides to calculate the probability of randomly selecting 15 songs, if One Thing, What Makes You Beautiful, and Live While We’re Young must be included in the CD.

Answer: This is a combination because order of the songs does not matter.

Probability = 3C3 * 17C12

                            20C15

                   =  91

                      228

∴ the probability Kelvin will include the three songs (One Thing, What Makes You Beautiful, and Live While We're Young) in the CD is 91/228. 

1.  One Thing 
2. What Makes You Beautiful 
3. Live While We're Young
   

Permutations

Cynthia is mad at Kelvin because he messed up the arrangements of the CD. She prefers to have One Thing, What Makes You Beautiful and Live While We’re Young to be together as the first, second and third tracks, respectively. Kelvin decides to burn a new CD. He calculates the number of arrangements is in total if the three singles must stay together.

Answer: This is a permutation because order is important. Moreover, the problem represents the number of ordered arrangement of 12 songs.

12! = 4.8*10⁸ arrangements

∴ there are 4.8*10⁸   arrangements in total with the three singles having to stay together as the first three tracks of the album.

University Choices

Multiplicative Principle

As of right now, we got accepted to Carleton University and to Brock University. Kelvin received scholarship offers from the two universities, $12,000 from Carleton and $8,000 and an iPad from Brock. Cynthia only got a scholarship offer from Brock worth $750. LOL!!! The probability that Kelvin chooses Carleton is 5/8. The probability that he chooses Brock is 3/10. The probability that Cynthia chooses Carleton is 1/5. The probability that she chooses Brock is 3/4.

If Kelvin decides to go to Carleton, the probability that Cynthia will follow him is 7/10. If Cynthia decides to go to Brock, the probability that Kelvin will follow her is 3/5. Our parents prefer that we go to the same school but ultimately, we decide which school to go to. We tried to figure out what is the probability that we end up at the same school based on which school we prefer to go to.

Answer: Using multiplicative principle because we are determining the probability of event A and B occurring given that event A is chosen.

A = Kelvin going to Carleton

B = Cynthia going to Carleton

Probability that we attend Carleton:

P(A∩B) = P(B|A) * P(A)

              = 7/10 * 5/8

              = 7/16

C = Cynthia going to Brock

D = Kelvin going to Brock

Probability that we attend Brock:

P(C∩D) = P(D|C) * P(C)

              = 3/5 * 3/4

              = 9/20

 ∴ the probability both of us going to Carleton together is 7/16 and probability of us attending Brock is 9/20.