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Chapter 12: Q30. (page 636)

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

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information.

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

02

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 10×1×9=90 numbers between 100 and 999, inclusive, that have 7 in the tens place.

03

Step 3. Conclusion.

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

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