Question

How many numbers greater than $ 24000 $ can be formed by using digits $ 1,2,3,4,5 $ when no digits are repeated?
 $ 1)36 $
 $ 2)60 $
 $ 3)84 $
 $ 4)120 $

Answer 1

Hint: First, we shall analyze the given data so that it can be easy for us to solve the problem. We are given five-unit digits $ 1,2,3,4,5 $ that can be used to make the numbers that are greater than $ 24000 $ . Follow the given step-by-step solution to solve the problem.
If once the digit is used then it will not be repeated again.

Complete step by step answer:
The given digits are $ 1,2,3,4,5 $
Since we need to find the numbers that are greater than $ 24000 $ , the first digit cannot be the digit $ 1 $ (which is less than the given number)
If the digit in the ten thousand places is $ 2 $ :
The number of possible digits for ten thousand places is $ 1 $ (that is a digit $ 2 $ )
The number of possible digits for thousands of place is $ 2 $ (they are digits $ 4,5 $ )
The number of possible digits for hundred places is $ 3 $ (they are any digits which are not used)
The number of possible digits for tens place is $ 2 $ (they are any digits which are not used)
The number of possible digits for one’s place is $ 1 $ (they are any digits which is not used)
Hence, the total possible combination is $ 1 \times 2 \times 3 \times 2 \times 1 = 12 $
If the digit in the ten thousand places is $ 3,4,5 $ :
The number of possible digits for ten thousand places is $ 3 $ (that is a digit $ 3(or)4(or)5 $ )
The number of possible digits for thousands of place is $ 4 $ (they are any digits which are not used)
The number of possible digits for hundred places is $ 3 $ (they are any digits which are not used)
The number of possible digits for tens place is $ 2 $ (they are any digits which are not used)
The number of possible digits for one’s place is $ 1 $ (they are any digits which is not used)
Hence, the total possible combination is $ 3 \times 4 \times 3 \times 2 \times 1 = 72 $
Therefore, combining the values we get, $ 12 + 72 = 84 $

So, the correct answer is “Option C”.

Note: For constructing the five-digit number, the first digit cannot be the digit $ 1 $ since we need to find the numbers that are greater than $ 24000 $
Since repetition is not allowed, if we use the number $ 2 $ then this same number will not be repeated in the process.