How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?

It can be written 60 different three digit numbers.

Step-by-step explanation:

For, calculate how many different three digit numbers can be written, we can use the rule of multiplication as:

    5              *         4         *             3                =      60

   1st digit         2nd digit          3rd digit

Taking into account that there is no repeating digits, we have 5 options for the first digits, this options are the number 5, 6, 7, 8 or 9. Then, we have 4 options for the second digit and then we have 3 options for the third digit.

So, there are 60 different three digit numbers that we can create with the set  5, 6, 7, 8, 9 without any repeating digits.