Question

Find the sum of all 4 digit numbers formed by taking all the digits 2,4,5,7

Answer 1

Answer:

18

Step-by-step explanation:

2+4+5+7=18

6+12=18

18=18

Answer 2

Answer:

The sum of all the 4 digit numbers formed by taking 2,4,5,7 is 119988

Step-by-step explanation:

1) Step 1:

Find the number of such four digit numbers formed by taking 2,4,5,7.

By permutations, the answer will be 4! = 24

Explanation: The first place will have 4 possible entries then second place will have 3 possible entries, excluding the one used in first place and so on 3rd place will have 2 possible entries and 4th place will have one possible entry

The no. of 4 digits numbers formed by taking 2,4,5,7 =

$= 4 \times 3 \times 2 \times 1$

$= 24 = 4!$

2) Step 2:

Finding the sum

Now in all these 24 numbers each of the number out of 2,4,5,7 will appear 6 times in all of the 4 places.

i.e. number 2 will appear 6 times in units place, 6 times in tens place, 6 times in hundreds place and 6 times in thousands place, total 24. Similarly for rest 3 numbers

So the sum of each digits place will be

$6 \times (2 + 4 + 5 + 7)$

$= 6(18)$

$= 108$

now by using simple method of addition will be find the sum,

T. H. T. U.

_ _. _. _

+

......(24 times)

+

_. _. _. _

individual sum of each place=

108 108 108 108

1) As the sum of units place digits is 108, the last digit of sum will be 8 and 10 will be carry forward to tens place

2) In the tens place the sum is already 108 and now additional 10 will be added from the units place sum so the final sum becomes 108 + 10 = 118, from this 8 will be the final second last digit of sum and rest 11 will be carry forward to hundreds place.

3) Similarly in the hundreds place, the sum will become 108+11= 119, 9 will be the final third last digit and 11 will be carry forward to thousands place

4) Lastly in the thousands place, the sum will become 108+ 11 = 119, now as the all the numbers we are adding are formed of 4 digits only, 10 thousands place is not there, so 11 will not be carry forward this time.

So the Final Sum becomes

= 119988

So the sum of all the 4 digit numbers formed by taking 2,4,5,7 only is 119988