3. (20) The Republic\'s Clone (later changed to the Empire\'s Clone football tea
ID: 3147260 • Letter: 3
Question
3. (20) The Republic's Clone (later changed to the Empire's Clone football team after the execution of Order66) football team has 53 players on the team. Since they've been cloned from Jango Fett and trained identically, they all have exactly the same skill level at every position. The players have been conveniently named #1, #2, , #53. How many different ways are there to create a group of 11 players to play? If we consider each position unique, how many different ways are there to create a lineup of 11 players? 4. (20) The Boogie Down Productions classic Criminal Minded contains 11 earth-rocking tracks. Public Enemy's It Takes a Nation of Millions has 16 ear-piercing tracks. A Tribe Called Quest's Peoples' Instinctive Travels & the Paths of Rhythm contains 14 smooth explorations in rhythm and rhyme. If you were to choose a group of 12 songs (where order doesn't matter), how many possible groups are there? If you wanted to create an ordered playlist for a local radio station with 5 songs from the first album, then 4 songs from the second album, and then 3 songs from the third album, how many possible sets are there? Not sure how to go at these, the chapter is focusing on permutations and combinations. If work was shown it woul dbe greatly appreciated!Explanation / Answer
(a) Total number of players = 53
No of players to be chosen = 11
No of ways of chosing a team, [order doesn't matter]= 53C11
No of ways of chosing a lineup, [order does matter as positions are unique]= 53P11
(b) No of tracks in album 1 = 11
No of tracks in album 2 = 16
No of tracks in album 3 = 12
No of ways of choosing 12 songs [order doesn't matter] = (11+16+12)C12 = 39C12
No of ways of making ordered playlist with 5 songs from album 1, 4 songs from album 2, 3 songs from album 3 = 11P5 * 16P4 * 12P3
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