Please answer this question wtih exact value - Interesting Question?

Question

A five digit number is formed using digits 1,3,5,7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

Answer 1

Hi,

To fill 5 spaces with 5 numbers, there are 5! or 120 ways to do it. Since the numbers are equally spaced, 1 and 9 average to 5 just as 3 and 7 average to 5, so if you replace the 1,3,7,and 9 in any number with a 5, then adding up 120 of the number 55555 will give the same total of 6666600. That's your answer.

You can see this principle if you do the same for 3 digit numbers using 1, 2, and 3. They would give the numbers:
123 + 132 + 213 + 231 + 312 + 321 = 1332
This is the same as 3! or 6 x 222 = 1332

I hope that helps!! :-)

Answer 2

The sum of numbers S = 25
4! numbers can be formed with a particular digit fixed.
So,sum of all 5 digit numbers formed from these digits =
4! * 25( 10000+1000+100+10+1)
= 6,666,600

This should be the answer.

Answer 3

5*4*3*2*1 = 120
1 + 3 + 5 + 7 + 9 = 25
120*25 = 3,000
edit:
I might learn to read some day!
11111 + 33333 + 55555 + 77777 + 99999 =
25 + 250 + 2500 + 25000 + 25000 + 250000 =
2777775
120*2777775 = 333,333,000

Answer 4

Each digit will appear in each position an equal number of times (24), so you can really look at it like this:

24*(11111 + 33333 + 55555 + 77777 + 99999) = 6666600

Answer 5

3000

Answer 6

375

Answer 7

277775