Suppose you have 18 objects (10 of type A, 5 of type B, and 3 of type C). Objects of type A are indistin- guishable from each other; objects of type B are indistinguishable from each other; and objects of type C are indistinguishable from each other. In how many ways can you: 1. Put the 18 objects in a row? 2. Pick 3 of the 18 objects (order does not matter)? 3. Pick 4 of the 18 objects (order does not matter)? 4. Pick 5 of the 18 objects (order does not matter)? 5. Pick nine objects out of the 18 objects so that exactly three objects are of type A and exactly two objects are of type B (order does not matter)?

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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.