1) You own 6 songs by Adele, 4 by Katy Perry, and 5 by Lady Gaga. How many diffe

Question

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?

Explanation / Answer

1)

here number of ways to make playlists =M(for each Adele song there are 6 choice; for each Perry song 4 choices and for each Lady Gaga song 5 choices)=64*43*52 =1296*64*25=2073600

2)

number of ways 10 participants are sitting =10! =3628800

number of ways partiicipants are sitting so that Kevin and Walter sits together =2*9! =727760

hence ways so that Kevin and Walter do not sits together=3628800-727760=2901040

3)

numebr of ways =6! =720

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