How many three-digit numbers can be made from the numbers 1, 2,3,4,5 if: a) the numbers are not repeated? b) can the numbers be repeated?
There are 5 different ways to select the first digit (left in a three-digit number). After the first place is taken, for example, by the number 2, there are four digits left to fill the second place. A choice of three numbers remains to fill the third place. Therefore, according to the multiplication rule, there is 5. 4 . 3 = 60 ways of arranging numbers, that is, the required number of three-digit numbers is 60. (Here are some of these numbers: 243, 541, 514, 132, …) It is clear that if the numbers can be repeated, then there are 5 three-digit numbers. five . 5 = 125. (Some of them are: 255, 333, 414, 111, …)