Question

What is the sum of all 5 digit numbers which can be formed with digits 0, 1, 2, 3, 4 without repetition

• A. 2599980
• B. 2679980
• C. 2544980
• D. 2609980

Answer 1

The correct option is A 2599980

Total number of 5 digit numbers (including which begins with zero) $=5!=120$Number of 5 digit numbers which begin with zero $=4!=24$
Sum of all 5 digit numbers
$=(0+1+2+3+4)\times 4!\times \left(11111\right)$
$=240\times 11111=2666640$
Sum of all five digit numbers which begin with zero
$=(1+2+3+4)\times 3!\times \left(1111\right)=66660$
Hence the sum of the required numbers $=sum$ of all 5 digit numbers including those numbers
which begin with zero $-sum$ of all 5 digit numbers which begin with zero.
$=2666640-66660=2599980$