Question

The number of numbers greater than $3000$, which can be formed by using the digits $0,1,2,3,4,5$ without repetition is

• A. $1240$
• B. $1280$
• C. $1320$
• D. $1380$

Answer 1

The correct option is D

$1380$

Explanation for the correct option:

Finding the number of numbers greater than $3000$, which can be formed by using the digits $0,1,2,3,4,5$ without repetition is:

Given digits: $0,1,2,3,4,5$

There are $6$. numbers in total

Number of $4$ digits number that is greater than $3000=3x5x4x3=180$

Number of $5$ digits number that is greater than $3000=5x5x4x3x2=600$

Number of $6$ digits number that is greater than $3000=5x5x4x3x2x1=600$

Therefore the number of numbers greater than $3000=180+600+600=1380$

Hence the correct answer is option (D).