# How many numbers having up to 4 digits exist such that sum of digits is up to 7?

Table of Contents

- 1 How many numbers having up to 4 digits exist such that sum of digits is up to 7?
- 2 How many four digit numbers are formed with no digit repeated?
- 3 How many 5-digit numbers have an even sum of digits?
- 4 How many values can be found in a 4 digit number?
- 5 How many four-digit numbers does 9+1+0+0 correspond to?

## How many numbers having up to 4 digits exist such that sum of digits is up to 7?

There are a total of 444 numbers .

## How many four digit numbers are formed with no digit repeated?

II : The sum of all four digit numbers that can be formed with 1,2,3,4 so that no digit being repeated in any number is 66660.

**How many 4 digit numbers are there when a digit may be repeated any number of times?**

Since repetition is allowed. So there are 9 × 10 × 10 × 10 = 9000 4-digit numbers when a digit may be repeated any number of times.

### How many 5-digit numbers have an even sum of digits?

But, we are interested in the numbers whose sum is even so it will be half of the total five digit numbers, so the answer is 1 2 × ( 9 × 10 × 10 × 10 × 10) which is 45000. There are 90000 5 -digit numbers, exactly half have an even sum of digits (base 10 has equal numbers of even and odd digits)

### How many values can be found in a 4 digit number?

It is a standard problem based on a technique called Star and Bar method.consider 4 digits as 4 boxes which can hold values 0,1,2…,9.but since u are concerned strictly of 4 digit numbers u can have only 1 to 9 in the first box or the first digit.

**How many ways can you choose the first digit of a number?**

The first digit can be chosen in 9 ways (since it can’t be a 0), the second in 10 ways, the third in 10 ways, the fourth in 10 ways, and the fifth in five ways (the last digit must be one of the five even digits if the first four digits add up to an even number, and odd otherwise, so that the total sum is even).

## How many four-digit numbers does 9+1+0+0 correspond to?

For each such sum, you can easily calculate how many four-digit numbers it corresponds to, considering that they can’t begin with a zero. Thus, 9+1+0+0 will correspond to 9100, 9010, 9001, 1900, 1090, 1009 — eight possibilities in all; likewise for 8+2+0+0, 7+3+0+0 and 6+4+0+0, while 5+5+0+0 will yield only the three possibilities 550