A folk festival is hosting a variety of different genres of music with a number of bands within each genre. There are 3 genres playing, Rock, Country, and Blues. There are 6 different rock bands, 4 different country bands, and 7 different blues bands. The festival is organized so that all bands within a given genre must play in a row before switching to another genre of music to help with scheduling. The order of the bands within each genre can change, and the order in which the 3 genres play can change as well. In how many total possible orders can all of these bands play? Be sure to write down your answer carefully as it may be quite large.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
A folk festival is hosting a variety of different genres of music with a number of bands within each genre. There are 3 genres playing, Rock, Country, and Blues. There are 6 different rock bands, 4 different country bands, and 7 different blues bands. The festival is organized so that all bands within a given genre must play in a row before switching to another genre of music to help with scheduling. The order of the bands within each genre can change, and the order in which the 3 genres play can change as well.
In how many total possible orders can all of these bands play? Be sure to write down your answer carefully as it may be quite large.
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