Chapter 15.5, Problem 4WE

To determine

To calculate: The number of even 3-digit positive integers with digits 1, 2, 4, 7 and 8.

Answer to Problem 4WE

The number of even 3-digit positive integers with digits 1, 2, 4, 7 and 8are $75$ .

Explanation of Solution

Given information:

Even 3-digit positive integers with digits 1, 2, 4, 7 and 8 are to be formed.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that even 3-digit positive integers with digits 1, 2, 4, 7 and 8are to be computed.

Let even 3-digit positive integer be $\boxed{}\boxed{}\boxed{}$ .

To select the first digit at one’s place, choices are between 2, 4 and 8 because these are evennumbers $\boxed{}\boxed{}\boxed{3}$ .

There are 5 possible options for tenths and hundredths place digit $\boxed{5}\boxed{5}\boxed{3}$ .

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $5\times 5\times 3=75$

Thus, the number of even 3-digit positive integers with digits 1, 2, 4, 7 and 8are $75$ .