IIT JEE , AIEEE Forum - Mathematics , Algebra - the sum of 4 digit numbers formed by 1,2,4 &6 is?

akhileshsk

the sum of 4 digit numbers formed by 1,2,4 &6 is?

akhil_o

first place 1 no. in the units place...
for each no in unit, we have 3! nos...
hence sum in units place for that no is

3!*n
so units place we have
3!(1+2+4+6)
=6(13)=78

now for 10s place,we have similarly the same no..
so total=78...but since it is 10s place sum value=78*10=780
similarly for 100s place-7800
and 1000s=78000
so total
78000+7800+780+78
=86658

sboosy

simple formula ...(for numbers without repetition)

sum of digits formed by n non zero digits is

(sum of digits) * (n-1)! (10ⁿ-1)/(10-1)

1,2,4,6 are the given digits

we get

(1+2+4+6)*(4-1)! * (10⁴-1)/(10-1)

13*6*9999/9

= 86658

this happens to be double of what akhil has got..

pls correct if any

akhil_o

sorry...calculation error...sboosy s ans is right..
took 6*13=39!!!
edit above..both methods r right

edison

Sol) The total no. of 4 digit numbers formed by 1,2,4 & 6 is 4!

i.e 24 combinations are possible. All digits occur 6 times at all places

Thus sum of digits at each place is (1+2+4+6) x 6 = 78

Thus sum of all digits at units place = 78

(Thus digit at ones place = 8)

Sum of all digits at tens place = 78 + 7 = 85

(Thus digit at tens place = 5)

Sum of all digits at Hundred's place = 78 + 8 = 86

(Thus digit at Hundred's place = 6)

Sum of all digits at Thousand's place = 78+8 = 86

Thus the sum is = 86658

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