Discrete Math: Suppose a license plate is made up of 2 letters from A to Z (26 letter alphabet) followed by 4 digits from 0 to 9. How many license plates are there if: (a) There are no restrictions? (b) There can be no repeated letter or digit? (c) The license plate must start with A and end with 8? (Repeats are allowed.)
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.
Discrete Math:
Suppose a license plate is made up of 2 letters from A to Z (26 letter alphabet) followed by 4 digits from 0 to 9. How many license plates are there if:
(a) There are no restrictions?
(b) There can be no repeated letter or digit?
(c) The license plate must start with A and end with 8? (Repeats are allowed.)
(d) The license plate must start with A or end with 8?
(Type your answers below. You DO NOT need to compute the number, e.g. 34 * C(8,3) would be fine.)
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