Chapter 15.5, Problem 10WE

To determine

To calculate: The number of ways to write a 3-digit positive integer.

Answer to Problem 10WE

The number of ways are $60$ .

Explanation of Solution

Given information:

Digits to form a 3-digit positive integer are 1, 3, 5, 7 and 9. No digit is repeated twice.

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 digits to form a 3-digit positive integer are 1, 3, 5, 7 and 9. No digit is repeated twice.

Let 3-digit positive integerbe $\boxed{}\boxed{}\boxed{}$ .

To select the first digit at hundredths place, there are 5ways $\boxed{5}\boxed{}\boxed{}$ .

Now no digit is repeated. Remaining are 4 digits. One digit is already used.

To select the second digit, there are 4ways $\boxed{5}\boxed{4}\boxed{}$ .

Now no digit is repeated. Remaining are 3 digits. Two digitsare already used.

To select the third digit, there are 3ways $\boxed{5}\boxed{4}\boxed{3}$ .

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,

  $5\times 4\times 3=60$

Thus, the number of ways to select 3-digit positive integer where repetition is not there are $60$ .