access code for the entrance of a faculty office consists of five digits. Each digit can be 0 through 9. How many access codes are possible if: Each digit can be used only once and not repeated? Each digit can be repeated? 0 cannot be the first digit and each digit can be repeated? a. # of Access codes = b. # of Access codes =
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.
- Each digit can be used only once and not repeated?
- Each digit can be repeated?
- 0 cannot be the first digit and each digit can be repeated?
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