i Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g. '924 VXA' or 4 digits followed by 2 (uppercase) letters, e.g. '2012 CS'. How many different license plates are possible? ii Henry owns 3 hiking shoes and 5 running shoes for his left foot. He owns 12 running shoes for his right foot. How many different pairs' of shoes, one left and one right, can he form?
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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