Question

1 2 3 and 4 can form 256 different four digit numbers. if digits repeated two of them are 1111 and 1113. then find the sum of 256 numbers.

Answer 1

Number of digits = 4

Total possible number of arrangement = 4 x 4 x 4 x 4 = 256

Group { 1, 2, 3, 4 }  as 1 set

⇒ Number of sets = 256 ÷ 4 = 64

Value of 1 set = 1 + 2 + 3 + 4 = 10

⇒ Value of 64 sets = 10 x 64 = 640

At ones place, the sum of all the digits = 640 x 1 = 640

At tens place, the sum of all the digits = 640 x 10 = 6400

At hundreds place, the sum of all the digits = 640 x 100 = 64000

At thousands place, the sum of all the digits = 640 x 1000 = 640000

Total sum = 640000 + 64000 + 6400 + 640 = 711040

Answer: The sum is 711040