How many two-digit prime numbers can be formed by choosing two different digits from the set 2, 7, 8, 9 to be used as the tens digit and units digit?
To form a two-digit prime number, the tens digit cannot be 0 or an even number, and the units digit cannot be even because if it is, the number would be divisible by 2.
Out of the 4 available digits (2, 7, 8, 9), only 2 and 7 are prime numbers.
So there are 2 choices for the tens digit (2 or 7) and 3 choices for the units digit (7, 8, 9).
Therefore, the total number of two-digit prime numbers that can be formed is 2 * 3 = 6.
The two-digit prime numbers that can be formed are: 27, 29, 72, 79, 89, 97.