Question

The sum of the digits in the unit's place of all numbers formed with the help of $3,4,5,6$ taken all at a times is

• A. $18$
• B. $432$
• C. $108$
• D. $144$

Answer 1

The correct option is C $108$

Let 3 be the unit place number, then there are 3 choices for 10th place number, as the 10th place digit can be chose from 4, 5, 6. Similarly there are 2 choices form 100th place digit and 1 choice for 1000th place digit.
Hence there are $3\cdot 2\cdot 1=6$ numbers ending with 3. These 6 number will add $6\times 3=18$ to the sum of the digits in the unit's place.
Similarly, there will be 6 numbers each ending with 4, 5 and 6 and they will add $4\cdot 6=24$; $5\cdot 6=30$ and $6\cdot 6=36$ to the sum.
Hence, the sum of the digits in the unit's place of all numbers formed with the help of $3,4,5,6$ taken all at a times is $18+24+30+36=108$.