Suppose that I want to arrange the following albums, given below by genre: (i) H
ID: 3359594 • Letter: S
Question
Suppose that I want to arrange the following albums, given below by genre:
(i) Hard Rock: 12 by Led Zeppelin and 4 by Deep Purple.
(ii) Progressive Rock: 11 by Genesis, 16 by King Crimson, and 33 by Yes.
(iii) Psychedelic Rock: 3 apiece by Cream and Jimi Hendrix, and 1 by Pink Floyd.
How many ways can I arrange these so all albums of a genre and all albums from a given artist/group stay together?
Suppose that I want to arrange the following albums, given below by genre: (i) Hard Rock: 12 by Led Zeppelin and 4 by Deep Purple. (ii) Progressive Rock: 11 by Genesis, 16 by King Crimson, and 33 by Yes (ii) Psychedelic Rock: 3 apiece by Cream and Jimi Hendrix, and 1 by Pink Floyd. How many ways can I arrange these so all albums of a genre and all albums from a given artist/group stay together?Explanation / Answer
group (i) can be arranged as follows:
Albums of Led Zeppelin can be arranged in 12! ways and albums of Deep Purple can be arranged in 4! ways. So Hard rock group can be arranged in 12!*4! ways.
Likewise group (ii) can be arranged in 11! *16!*33! ways
Likewise group (iii) can be arranged in 3! *1! ways
Three genre can be arranged in 3! ways.
So required number of arrangements is
12!*4! * 11! *16!*33! *3! *1!*3!