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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.
A Cryptarithm The following puzzle is a famous cryptarithm.
Each letter in the cryptarithm represents one of the digits 0 through 9. The leading digits, represented by S and M, are not zero. Determine which digit is represented by each of each of the letters so that the addition is correct. Note: A letter that is used more than once, such as M, represents the same digit in each position in which it appears.
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