Question

find the sum of all possible four digit numbers that can be formed using the digits 2,4,5,6,7 and 8 with no repeated digits

Answer 1

1+1
2+2
5+0
3+3
6+2-1
4+4

Answer 2

2133120

Explanation:

using 6 given digits, lets create a 4 digit number:

to choose the first number, you have 6 options. to choose the second number we have 5 options left. for the third number we have 4 options left. and for the fourth number, we have 3 options left.

6*5*4*3 = 360

with no repeats, 360 numbers can be formed.

this means that each number will occur 60 times each (360/6 digits)

so to find the sum:

60*(2+4+5+6+7+8) = 1920

but, we have one more thing:

In the thousands place, our sum of digits is multiplied by 1000; in the 100’s place, by 100; in the ten’s place, by 10; and in the one’s place, by 1. so:

1920(1000+100+10+1) = 1920*1111 = 2133120