Using the digits 1, 3, and 5, Mônica forms three-digit numbers that are greater than 150. How many numbers can Mônica form?

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Solution

There are three possibilities for the first digit of the number formed by Mônica.

a) The hundreds digit is 1. For the number to be greater than 150, the tens digit must be 5. There are only three options left for the units digit, namely: 1, 3, or 5. In this case, she can form only 3 numbers.

b) The hundreds digit is 3. For any choices of the tens and units, the number formed will be greater than 150. Since there are three options for the tens and three for the units, the total number of numbers in this case is $3 \cdot 3=9$.

c) The hundreds digit is 5. As in the previous case, for any choices of the tens and units, the number formed will be greater than 150. There are 9 numbers in this case.

Therefore, the total number of three-digit numbers that Mônica can form is $3+9+9=21$.