A 3-digit code is to be made from the set of digits {4, 5, 6, 7, 8}. a. How many codes can be formed if there are no restrictions? b. How many codes can be formed if the corresponding 3-digit number is to be an even number? c. How many codes can be formed if the corresponding 3-digit number is to be a multiple of 5 and there can be no repetition of digits?
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 3-digit code is to be made from the set of digits {4, 5, 6, 7, 8}.
a. How many codes can be formed if there are no restrictions?
b. How many codes can be formed if the corresponding 3-digit number is to be an even number?
c. How many codes can be formed if the corresponding 3-digit number is to be a multiple of 5 and there can be no repetition of digits?
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