Find out the quantity of four-digit numbers that can be created by utilizing the digits from 1 to 9 if repetition of digits is not allowed? 

This question was previously asked in
AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 3)
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  1. 1680
  2. 336
  3. 3036
  4. 3024

Answer (Detailed Solution Below)

Option 4 : 3024
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Detailed Solution

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Given:

4 digit numbers that can be created by utilizing the digits from 1 to 9. if repetition of digits is not allowed then,

Formula Used:

nPr = \(\frac{n!}{(n - r)!}\)

Calculation:

n = numbers from 1 to 9 = 9

r = 4 

Required 4-digit number = 9P4

⇒ \(\frac{9!}{(9 - 4)!}\)

⇒ \(\frac{9!|}{5!}\)

⇒ \(\frac{ 9 \times 8 \times 7 \times 6 \times 5!}{5!}\)

⇒ 3024

∴ The quantity of four-digit numbers that can be created is 3024.

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