You have 6 different Algebra books, 5 different Biology books, 4 different Chemistry books, and 3 different copies of the novel Dune. In how many distinct ways can you arrange a) 10 books on a shelf if exactly 4 must be Algebra books? b) all of the books on a shelf if the copies of Dune must be on the ends
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.
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