Question

How many four-digit numbers are possible using the digits 1, 3, 5 and 7 without repeatition?​

• A. 24
• B. 26
• C. 22
• D. 28

Answer 1

The correct option is A 24

We know that, systematic listing helps in listing of all possible outcomes for an event in an organised/systematic way.

The possible numbers where 1 is at the thousands place are : 1357, 1375, 1537, 1573, 1735, 1753.

The possible numbers where 3 is at the thousands place are: 3157, 3175, 3715, 3751, 3517, 3571.

The possible numbers where 5 is at the thousands place are: 5137, 5173, 5317, 5371, 5713, 5731.

The possible numbers where 7 is at the thousands place are: 7135, 7153, 7315, 7351, 7531, 7513.

$\therefore$ there are 24 possible numbers that can be made using the given digits.