Solution:
Given the numbers 2, 3, 5, 7, 8, 9.
We are interested in knowing how many different 2-digit numbers can be interchanged with the given numbers.
Total numbers = 6
For the first digit, any of the six numbers can occupy the position.
For the second digit, any of the six numbers can also occupy the position,
Thus,
Number of different 2-digit numbers that can be formed from these numbers = 6 x 6 = 36
The answer is 36