You want to take the 21 books not on your shelf and give them to your 4 friends. In how many ways can you partition the books among the 4 friends where it may be that some friends get no books? Note that all 21 books are unique.
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.
(1) You want to take the 21 books not on your shelf and give them to your 4 friends. In how many ways can you partition the books among the 4 friends where it may be that some friends get no books? Note that all 21 books are unique.
(2) You come across a stash of 25 copies of To Kill a Mockingbird. Since you already have a copy on your shelf, you decide to donate them to the local high schools. There are 3 high schools in your town. In how many ways can you distribute the books to the high schools? Note that it is possible that a high school gets no books.
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