Five country music bands and 3 rock bands are signed up to perform at an all-day festival. How many different orders can the bands play in if the following conditions apply? (a) there are no restrictions on the order (b) all the bands of each type must perform in a row?
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.
Five country music bands and 3 rock bands are signed up to perform at an all-day festival. How many different orders can the bands play in if the following conditions apply?
a) Given that there are 5 country music bands and 3 rock bands. So total (5+3)=8 bands
If there are no restrictions then we can arrange the 8 bands in 8!=
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