**Question: **

What is the sum of all the four digit numbers formed using the digits 0, 1, 2 and 3. None of the two digits should be repeated?

**Answer:**

From these four digits '0' cannot be at first place to form four digit number

so we have 1, 2, or 3 can be at thousand's place

keeping one digit at thousand place can have 6 different four digit number

so that means

1000*6 + 2000* 6 + 3000* 6 = 36000

Now come to hundred's place we can have all four digit at this place , '0' will not contribute any thing to sum so in all four digits number 1,2,3 will be at 4 times on same place

so that means

100*4 + 200* 4 + 300 * 4= 2400

Now come to tenth's place ...same as hundred

so

10*4 + 20*4 + 30*4= 240

same for unit place

1*4 + 2*4 + 3*4= 24

in last if you add whole the total sum of all possible four digit number formed is 38664