In: Statistics and Probability
1) You own 6 songs by Adele, 4 by Katy Perry, and 5 by Lady Gaga. How many different playlists can you make that consist of 4 Adele songs, 3 Perry songs, and 2 Gaga songs, if you do allow repeated songs?
2) Kevin and Walter can't stop discussing their Probability course at every opportunity, which has been very disruptive of the regular discussions at the CCIS Teaching Seminar. Martin, who organizes the seminar, must now calculate the number of ways in which he can arrange the 10 participants in a line so that Kevin and Walter aren't sitting next to each other. What is that number?
3) In a race with 6 runners, how many possible finishing orders are there?