Question

Suppose there are 29 songs in your itunes account, and you would like to make a playlist.

1. You would like to choose 11 different songs for your playlist. How many ways are there to create this playlist, where order in which you select songs matters?

2. Suppose you always use the random play function so that order in which you pick the songs on the playlist does not matter. How many ways are there to create a group of 9 songs from your itunes account?

3. Suppose you chose 5 country songs and 7 R&B songs on your playlist and play two songs at random. If each song plays with equal probability, what is the probability that you play two songs from the same genre?

Answer 1

1)

number of ways choose 11 from 29 and arrange in order=(29P11) =29!/(29-11)! =1.38*10¹⁵

2)

number of ways to select 9 from 29 =(29C9) =(29!/(9!*(29-9)!) =10015005
3)

probability that you play two songs from the same genre =P(both country songs )+P(both R &B songs)

=(5/12)*(4/11)+(7/12)*(6/11)

=31/66