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What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?

Correct Answer: 32640

Explanation:

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.


 


The formula to find sum of all numbers in a permutation is


 


111 x no of ways numbers can be formed for a number at given position x sum of all given digits


 


No of 1 s depends on number of digits


 


So,the answer us


 


111 x 20 x (0+1+2+3+4+5) = 33300


 


We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.


 


Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.


 


This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.


 


So the sum for this is 11 x 4 x (1+2+3+4+5).
=660


 


Hope u understood why we use 4. Each number can be formed in 4x1 ways


 


So, the final answer is 33300-660 = 32640


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