Question

How many numbers between 1,000 and 10,000 can be formed with the digits 1. 3.5.7.9. when each digit being used only once in each number?​

Answer 1

Answer:

2880

Step-by-step explanation:

Ways to choose 4 digits from the 5 digits is

5p4 = 5!/(5-4)! = 5! = 120

Now, other digits after the first digit can be made by

4p3 = 4! = 24

Now, total ways are 120 . 24 = 2880

Answer 2

Answer:

120 Numbers

Step-by-step explanation:

We need the find how many numbers can be formed using the digits: 1, 3, 5, 7 and 9 which lie between 1,000 and 10,000.

Any 4 digit number formed using these digits will always be greater than 1,000.

The amount of numbers possible will be:-

The ways in which 'Thousandth' digit place can be filled = 5
The ways in which 'Hundredth' digit place can be filled = 4
The ways in which 'Tens' digit place can be filled = 3
The ways in which 'Ones' digit place can be filled = 2

The available numbers decrease with places because numbers can't be repeated.

Therefore, quantity of numbers possible will be = $\sf 5 \times 4 \times 3 \times 2 = 120$

Any 5 digit number formed using these digits will always be greater than 10,000. Therefore, there are no cases where 5 digit numbers would be valid.

So, 120 numbers between 1,000 and 10,000 can be formed with the digits 1, 3, 5, 7 and 9 when each digit is used only once.