Latest TCS Aptitude Question SOLUTION: What is the sum of all 5 digit numbers which can be formed with the digits 0,1,2,3,4 without repetation? a)2599980 b)235500 c)923580 d)765432

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What is the sum of all 5 digit numbers which can be formed with the digits 0,1,2,3,4 without repetation?

a)2599980
b)235500
c)923580
d)765432

Asked In TCS Shristy kashyap (8 years ago)

Solved gourav Read Solution (16)

Is this Puzzle helpful?   (31)   (13) Submit Your Solution Permutation and Combination

Read Solution (16) :

ANKIT PATEL  (8 years ago)

10(11111)*4! - 10(1111)3! = 2599980

Is this solution Helpfull? Yes (29) | No (6)  

Bibek Dey  (8 years ago)

There are 4*4*3*2=96 such numbers. Leading digits can be 1,2,3 and 4 [24 occurrences each] . Other 72 numbers will 0's and hence 72*4-72=216 total occurrences of 1,2,3 and 4 in other places. 216/4=54 1's, 2's, 3's and 4's. [18 1's,2's,3's and 4's at hundredth, tenth and unit place.]
[1+2+3+4]*24*1000[occurrences at thousand's place]+[1+2+3+4]*18*[1+10+100]=259980

Is this solution Helpfull? Yes (8) | No (2)  

Deepika Mahulia  (8 years ago)

The formula is (n-1)![Sum of digits][No. of 1s]
n=No. of digits used
(5-1)![0+1+2+3+4][11111]=2666640

Is this solution Helpfull? Yes (8) | No (3)  

Soham Dey  (8 years ago)

The best solution approved here is not correct,the correct answer is option (a) 2599980,checked from two sources...

Is this solution Helpfull? Yes (6) | No (3)  

gourav  (8 years ago) Best Solution

ans is 923580 . it is because if we consider 1 as unit digit there are 3*3*2*1 cases so unit digit and similarly considering for 2,3,4,0 unit digit will be 18*1+18*2+18*3+18*4=180 , 18 will be the carry for ten's digit also it will be 180+18=198 ten's digit will be 8 and in options only c option has ten's digit 8.

Is this solution Helpfull? Yes (5) | No (45)  

Subhendu Pradhan  (8 years ago)

4*4!=96 ,five digit numbers are possible.at unit place,10th place, 100 place and 1000 place each digit is repeating 18 times but in 10000 place each digit is repeating 24 times(excluding zero)
hence, 18*1+18*2+18*3+18*4=180 so,unit digit will be 0 and 18 will be the carry for 10th place. similarly for 10th place 180+18=198, 8 will be 10th pace digit 19 will be the carry for 100 place.
in 10000 place 24*1+24*2+24*3+24*4=240 and 240+19(carry from 1000 place)=259
hence the ans. will be 2599980

Is this solution Helpfull? Yes (3) | No   

Girish kumar  (8 years ago)

There are 4⋅4⋅3⋅2=96 possible numbers (not 5⋅4⋅3⋅2, since the first digit must by nonzero). If you pick one at random, the expected value of the first digit is 1+2+3+44=5/2, and the expected value of each other digit must be 15/8, because the sum of all five digits is 0+1+2+3+4=5/2+4⋅15/8. By linearity of expectation, the sum of all 96 numbers is 96(5/2⋅1000+15/8⋅111)=259980.

Is this solution Helpfull? Yes (2) | No (2)  

Swathi.S  (6 years ago)

its a 5 digit number therefore (10000+1000+100+10+1)=11111
(0+1+2+3+4) (11111) (4!) - (0+1+2+3+4) (1111) (3!)
2599980

Is this solution Helpfull? Yes (2) | No   

Abhishek Kumar  (8 years ago)

Refer solutions on: http://www.quora.com/What-is-the-sum-of-all-4-digit-numbers-that-can-be-formed-by-the-digits-0-1-2-3-4-No-repetitions-allowed

There are 4⋅4⋅3⋅2=96 possible numbers (not 5⋅4⋅3⋅2, since the first digit must by nonzero). If you pick one at random, the expected value of the first digit is 1+2+3+44=52, and the expected value of each other digit must be 158, because the sum of all five digits is 0+1+2+3+4=52+4⋅158. By linearity of expectation, the sum of all 96 numbers is 96(52⋅1000+158⋅111)=259980.

Is this solution Helpfull? Yes (1) | No (1)  

Prashant Saini  (8 years ago)

lol !!! best solution approved here is actually wrong... RIP question poster :p

Is this solution Helpfull? Yes (1) | No   

Khushboo  (8 years ago)

(o+1+2+3+4+5)(11111)(4!)

Is this solution Helpfull? Yes | No (6)  

PUJA NAG  (8 years ago)

why 11111 is multiplied

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abhinav  (8 years ago)

what is the logic of multiplying 10 please explain @ANKIT PATEL

Is this solution Helpfull? Yes | No (1)  

Ravi bisariya  (8 years ago)

sorry m not understanding... plzz elaborate me ans with sol.

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VIVEK JAIN  (8 years ago)

Right answer is A

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VIVEK JAIN  (8 years ago)

2599980 is right answer

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