Question

What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?
A) 28450
B) 26340
C) 32640
D) 36450

Answer 1

Q:

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

A) 28450
B) 26340
C) 32640
D) 36450

Answer:   C) 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 is
 
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

Answer 2

What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?
A) 28450
B) 26340
C) 32640✔️✔️✔️

D) 36450