Table of Contents

- 1 How many three digit numbers can be generated using the digits 1 2 3 4 without repeating any digit?
- 2 How many numbers can be formed so that odd digits occupy odd places?
- 3 How many 3 digit numbers can be formed from the digits 1 2 3 4 and 5 assuming that 🙁 I repetition of the digits is allowed II repetition of the digits is not allowed 4 marks?
- 4 How many numbers are there in a 4-digit number?
- 5 How many combinations of 0-9 can be arranged into a 4-digit code?

## How many three digit numbers can be generated using the digits 1 2 3 4 without repeating any digit?

There are only two numbers left and the units place can be filled in 2 ways. Hence by fundamental counting principle, the total number of three digit numbers = 4 x 3 x 2 = 24.

## How many numbers can be formed so that odd digits occupy odd places?

The number of numbers that can be formed with the help of the digits 1, 2, 3, 4, 3, 2, 1 so that odd digits always occupy odd places, is. 18. 12.

**How many 3-digit numbers can be written using 1/2 and 3 What is the probability of the numbers with same digits?**

digits are 3, and number of places are 3. The calculation will be 3!/0!, which is equal to 3!= 6. So 6 3-digit numbers can be formed using 1,2,3!!!

**How many 3-digit numbers can be formed from the digits 1/2 and 3?**

So I take some particular numbers, like 1,2,3 and say that, well, 1 can go in 3 places, 2 in 2 places and 3 in 1 place, so by multiplication principle, there are 6 ways of forming a 3-digit number with 1,2,3. But there are 4 different numbers.

### How many 3 digit numbers can be formed from the digits 1 2 3 4 and 5 assuming that 🙁 I repetition of the digits is allowed II repetition of the digits is not allowed 4 marks?

Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Solution: Answer: 108. Let 3-digit number be XYZ.

### How many numbers are there in a 4-digit number?

There are 4 numbers (any number from 0-9) in a 4-digit number. There are 9000 four digit numbers in all.

**How many numbers can be formed from the second blank?**

The second blank can now be filled by four remaining digits because repetition is not allowed and hence the digit selected for the first blank cannot be selected. So four ways. Similarly 3 for the third blank and two for the last blank. Hence the answer is 120 such number can be formed.

**Do we work out 4 + 5 first then multiply by 3?**

We do NOT work out 4 + 5 first to get 9 and then multiply by 3. Example of Rule 1: (4 + 5) x 3 (4 + 5) x 3 is equal to 27, because we calculate the brackets first to 4 + 5 = 9 and then multiply by 3. We do NOT work out 5 x 3 and then add 4.

#### How many combinations of 0-9 can be arranged into a 4-digit code?

There are 10,000 possible combinations that the digits 0-9 can be arranged into to form a four-digit code. Berry analyzed those to find which are the least and most predictable.