we can build our 5 digit number using 5 different numerals
all possible numbers
= 5! or 120
In all of these, the lead digit, the 10-thousand digit, can be occupied by the "9" 24 times, the "8" 24 times, etc.
The value of those 24 9's would be
24(90000) = 24(9)10,000)
The value of those 24 8's would be
24(8)(10,000)
...
the value of those 24 1's would be
24(1)(10,000)
so the value of all the 5th digit numbers
= 24(9)(10,000) + 24(8)(10000) + .. 24(1)(10000)
= 24(10000)(9+8+6+3+1)
= 24(10,000)(27)
I could use the same argument for the thousand column
sum of all the 4th digit numbers
= 24(1000)(27)
....
same for the hundreds, the tens and the unit column
total
= 24(27)(10,000) + 24(27)(1000) + 24(27)(100) + 24(27)(10) + 24(27)(1)
= 24(27)(10,000 + 1000 + 100 + 10 + 1)
= 24(27)(11111)
= 7,199,928
What is the average of all possible five-digit numbers that can be formed by using each of the digits 8, 9, 1, 3 and 6 exactly once?
Are you just supposed to try out all the possibilities and count them or is there like a formula or something you can sub numbers into?
Thank you
1 answer
1 answer