Table of Contents

- 1 How many 5-digit positive integers are there?
- 2 How many positive integers are there with distinct digits?
- 3 How many 5-digit numbers are there whose sum of digits is odd?
- 4 How many integers between 100 and 999 have distinct digits and how many of those are odd numbers?
- 5 How many 5-digit even numbers are there?
- 6 How do you find the sum of the remaining 5 digits?
- 7 What is Camy’s list of integers?

## How many 5-digit positive integers are there?

There are 9 × 104 = 90000, 5-digit positive integers.

## How many positive integers are there with distinct digits?

1-digit integers: 1., 9 – there are 9 integers. 2-digit integers: 10., 99 – there are 90 integers, but in 9 of them (11., 99) the two digits are the same. So there are 90 − 9 = 81 2-digit integers with distinct digits.

**How many positive 4 digit integers are there?**

There are 4500 even 4 digit positive numbers.

**How many positive 5-digit integers have the odd sum of their digits?**

There are 45,000 5-digit positive integers whose digit-sum is odd. There are several ways to approach this problem, but this is (in my opinion) the most intuitive.

### How many 5-digit numbers are there whose sum of digits is odd?

Hence, the answer is (99,999–9,999)/2 = 45,000.

### How many integers between 100 and 999 have distinct digits and how many of those are odd numbers?

320

Hence there are 320 such numbers between 100 and 999 which are odd and have distinct digits. Note: Students should note that at hundreds place zero cannot be placed as no three digit number starts with zero and hence it can be filled by only 8 ways.

**How many integers are there from 100 through 999 have distinct digits?**

**How many distinct numbers are there between 1000 and 9999?**

Complete step-by-step answer: Number of natural numbers between 1000 and 9999 are (9999 – 1000 + 1) = 9000. Now, we will find all the 4 digits natural numbers with all unique digits. The first place of the number cannot have 0, therefore, the number of possibilities of the first place is 9.

#### How many 5-digit even numbers are there?

The correct answer is 13776. There are 3024 five-digit numbers that begin with the digit 4 with no repetition.

#### How do you find the sum of the remaining 5 digits?

So, to ensure that the SUM of the remaining 5 digits is divisible by 3, the digit that we remove must be divisible by 3. Removing 0 leaves us with the digits 1, 2, 3, 4, and 5, which have a sum of 15. Great. Removing 3 leaves us with the digits 0, 1, 2, 4, and 5, which have a sum of 12. Great.

**How many possible integers are there with ten thousands digits?**

Ten-thousands digit can be 1,2,4,5 = 4 choices. Number of ways to arrange the remaining 4 digits = 4! = 24. Number of possible integers = 4*24 = 96. Thus, total possible integers = 120+96 = 216. If you find one of my posts helpful, please take a moment to click on the “UPVOTE” icon.

**Can a 5 digit number be created with 0?**

IMPORTANT: IF we were to start listing 5-digit numbers that can be created with the digits 0, 1, 2, 4, and 5, we would have to ensure that the first digit is NOT 0. Otherwise, we’d get a 4-digit number (e.g., 02451 is NOT a 5-digit number).

## What is Camy’s list of integers?

Camy made a list of every possible distinct five-digit positive integer that can be formed using each of the digits 1, 3, 4, 5 and 9 exactly once in each integer. What is the sum of the integers on Camy’s list?