Q30. - Algebra 2

Question

How many numbers between 100 and 999, inclusive, have 7 in the tens place?

1. 90
2. 100
3. 110
4. 120

Step-by-Step Solution

Answer

A) There are 90 numbers between 100 and 999, inclusive, that have 7 in the tens place.

Step 1. Given Information.

It is to be determined how many numbers between 100 and 999, inclusive, have 7 in the tens place.

Step 2. Calculation .

The units place can have any number from 0 to 9. Hence there are 10 ways to select the units place.

The tens place can have only 7 i.e., 1 way.

 

The hundredth place can have any number from 1 to 9 (having 0 changes the number to two-digit number). Hence there are 9 ways to select the hundredth place.

By the Fundamental Counting Principle, there are $10\times 1\times 9=90$ numbers between 100 and 999, inclusive, that have 7 in the tens place.

Step 3. Conclusion .

Hence, there are 90 numbers between 100 and 999, inclusive, that have 7 in the tens place.