A fan of country music plans to make a custom CD with 12 of her 25 favorite songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination?
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 fan of country music plans to make a custom CD with 12 of her 25 favorite songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination?
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