Question

Sum of all four digit numbers that can be formed with the digits 3, 2, 3, 4 is

• A. 39966
• B. 39996
• C. 40996
• D. 40966

Answer 1

Answer: (B)

39996

Answer 2

Total number of four digit number formed = $\frac { 4 ! } { 2 ! }$ = 12

If 4 is at unit place, then number of numbers = $\frac { 3 ! } { 2 ! } = 3$

If 2 is at unit place, then number of numbers = $\frac { 3 ! } { 2 ! } = 3$

(In both cases, 3 is repeated twice)

If 3 is at unit place, then number of numbers = 3 ! = 6

∴ Sum of digit at unit place = 4 x 3 + 2 x 3 + 3 x 6 = 36

Similarly, sum of digit at 10^th, 100^th and 1000^th place = 36

∴ Required sum = (1000 + 100 + 10 + 1) = 39996