Question

\{1, 2, 3, 4, 5, 6\} Company X wants to assign each employee a 3-digit ID number formed from digits in the set shown above . No digit may appear more than once in an ID number , and no two employees may be assigned the same ID number. What is the greatest total number of different ID numbers?

Answer 1

The problem is asking for the number of unique 3-digit ID numbers that can be formed from the set {1, 2, 3, 4, 5, 6} where no digit may appear more than once in an ID number.

This is a permutation problem. In permutations, the order of selection matters. Here, the order in which the digits are selected matters because changing the order changes the ID number.

For the first digit of the ID number, we have 6 choices (any of the 6 digits). After we've chosen the first digit, we have 5 choices left for the second digit. Similarly, for the third digit, we have 4 choices left.

So, the total number of different 3-digit ID numbers that can be formed is 6 * 5 * 4 = 120.

Therefore, the greatest total number of different ID numbers that can be assigned is 120.