Chapter 15.5, Problem 3WE

To determine

To calculate: The number of odd 3-digit positive integers with digits 2, 3, 4, 5 and 6.

Answer to Problem 3WE

The number of odd 3-digit positive integers with digits 2, 3, 4, 5 and 6are $50$ .

Explanation of Solution

Given information:

Odd 3-digit positive integers with digits 2, 3, 4, 5 and 6 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 odd 3-digit positive integers with digits 2, 3, 4, 5 and 6 are to be computed.

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

Odd numbers are 1, 3, 5, 7 and 9.

To select the first digit at one’s place, choices are between 3 and 5because these are odd numbers $\boxed{}\boxed{}\boxed{2}$ .

There are 5 possible options for tenths and hundredths place digit $\boxed{5}\boxed{5}\boxed{2}$ .

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,

  $5\times 5\times 2=50$

Thus, the number of odd 3-digit positive integers with digits 2, 3, 4, 5 and 6are $50$ .