Elitmus
Exam
Numerical Ability
Permutation and Combination
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?
1.6666600
2.6666660
3.6666666
4.None
Read Solution (Total 7)
-
- Total Combinations without repetation is 5!=120.
smallest no = 13579 largest no = 97531.
take avg. = ((13579+97531)/2)*120= 6666600
ie ans is 1. - 10 years agoHelpfull: Yes(108) No(1)
- Ans: 6666600
Explanation:
Given digits are 1,3,5,7,9
I am writing the numbers are in ascending form.. from given digits, numbers should be:
97531 + 97513 + 97351 + ........+ 13759 + 13597 + 13579
Now we 'll add first and last term of above sequence and again we 'll add second and second last term and so on...
we 'll get
97531 + 13579 = 111110
97513 + 13597 = 111110
97351 + 13759 = 111110
..
..
Upto middle position of the above sequence.
Now we see every time we are getting 111110
now i have to find the how many possible number :
==> 5*4*3*2*1 = 120
there are 120 numbers
then the middle position is: 120/2 = 60
so, sum of all possible numbers are....
60*111110 = 6666600 Ans.
- 10 years agoHelpfull: Yes(27) No(2)
- 4!(1+3+5+7+9+)*11111
- 10 years agoHelpfull: Yes(14) No(4)
- Sum of arrangement of such numbers are given by:(n-1)!*n times 1*(sum of digits)
here n = 5 and (n-1)! = 4! = 24..
sum of (first 5 odd) digits = n^2 = 25
thus 24*11111*25 = 6666600..option 1) - 10 years agoHelpfull: Yes(9) No(0)
- ans is 1.6666600
total possible no without replacement 5!=120
how many time 1,3,5,7,9 occur at unit place
24 times
_ _ _ _ 1 (1*24 => 24)
_ _ _ _ 3 (3*24 => 72)
_ _ _ _ 5 (5*24 => 120)
_ _ _ _ 7 (7*24 => 168)
_ _ _ _ 9 (9*24 => 216)
24+72+120+168+216 = 600 {Extract '0' from 600 for sum of all possible no acting as a unit place..
so remain digit is 60.....Carry-1}
again how many time 1,3,5,7,9 occur at ten place
6 times
_ _ _ 1 (1*6 => 6)
_ _ _ 3 (3*6 => 18)
_ _ _ 5 (5*6 => 30)
_ _ _ 7 (7*6 => 42)
_ _ _ 9 (9*6 => 54)
6+18+30+42+54 => 150
now add 150 to carry 60
150+60 = 210...{Extract '0' from 210 for sum of all possible no acting as a Ten place..so remain digit is 21.....Carry-2}
doing in this way i got my ans 6666600.....
- 10 years agoHelpfull: Yes(4) No(3)
- sum of all such possible numbers formula=n*(n-1)!*11111
here n=5=5*4!*11111=6666600 - 10 years agoHelpfull: Yes(2) No(3)
- If you assume that any digit is in fixed position, then the remaining four digits can be arranged in 4! = 24 ways.
So, each of the 5 digit will appear in each of the five places 24 times. So, the sum of the digits in each position is 24(1+3+5+7+9) = 600
The sum of all such numbers will be 600(1 + 10 + 100 + 1000 + 10000) = 6666600 - 6 years agoHelpfull: Yes(0) No(0)
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