Question

what is the sum of all the five digit integers in which each of the digits 1 2 3 4 and 5 appear exactly once

Answer 1

3,999,960

Explanation:

1)let me take an example, the sum of all the digits numbers can be formed using the 1,2 without repetition.

(12, 21 ) , The sum is 12+21= 33

2)Another one, the sum of all the digits numbers, can be formed using three digits 1,2,3, without repetition.

(123,231,321,213,312,132) Their sum is by adding and is 1332

For the above example, we can find the answer by using the formula.

(n-1)! x sum of the digits x ( 111111111….n times)

For example, 1)

n = 2, the sum of the digits 2+1= 3

(2–1)! x3 (11)

1x 3 x 11= 33

For example 2

n= 3 sums of the numbers 1+2+3 = 6

(3–1)! x 6( 111)

2x1x6x111

12x111= 1332

Both answers verified

For the given question

n= 5 , sum of the digits 1+2+3+4+5=15

(5–1)! x 15 x 11111

4! x 15 x 11111

4 x 3 x x2 x 15 x 11111

24 x 15 x 11111

360 x 11111= 3999960

Answer: 3999960