How many 10 digit numbers are there whose sum of the digits is the number 4

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Priya

  • Jun 15th, 2005
 

13,31,40,22, so totally 4 ten digit numbers are there

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coco

  • Jun 29th, 2005
 

and 211,112,121,1021,if I can use 0,there are too many numbers to count.

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abhelaksh

  • Jul 20th, 2005
 

we have to make 10 digit nos using three cases: 
4 and rest all zeros = 1 
1,3 and rest all zeros = 9+9 
2,1,1 and rest all zeros = 36+..... 
2,2 and rest all zeros = 9 
1,1,1,1 and rest all zeros = 6 raised to par 4=1296 
 
then calculate the individual permutations for each case as shown above to get answer more than 1360

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krishnamurari

  • Aug 17th, 2005
 

I think that for four 1's to be in the 10 digit no. the answer should be 
 
9c3=9*8*7/(3*2*1)=84

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krishnamurari

  • Aug 17th, 2005
 

I think that for four 1's to be in the 10 digit no. the answer should be 
 
9c3=9*8*7/(3*2*1)=84

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Bhavik R Domadia

  • Sep 1st, 2005
 

The smallest 10 digit number is 1000000000 and the largest is 9999999999 and its difference is 8999999999. now dividing this number by 9 ( as there are 9 numbers from 1 to 9 ) the result is 999999999.89 .... hence 999999999 or 1000000000 seems to be the possible two answers ....  
 
because according to numerology ....  
 
Total of all digits of 1000000003 is 4 
 
Similarly Total of all digits of 9999999994 is 4 because when you add 9 any number n sum up its digits .... the total will be same .... so 9 doesnt have any significance .... as the result will be same if u add 9 or not 

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Prasanna

  • Sep 27th, 2005
 

Considering that the sum 4 can be divided as follows: 

                     Possibilities
4                       1
3 1                  18
2 2                  18
2 1 1                3 * (9c2) = 3 * (9 * 8/1 * 2) = 3 * 36 = 108
1 1 1 1            4 * (9c3) = 4 * (9 * 8 * 7/1 * 2* 3) = 84
                       ---
                        229 
                       ---

This can be the answer, provided the sum determined from adding patterns like 9 + 4 = 13...again 1 + 3 = 4 are not considered.

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sandeep

  • Jan 2nd, 2007
 

the answer is 220 .... prasanna is almost rt except for 2,2 for which the total number would be 9 and not 18 ... otherwise he is rt

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Marcus Uranus

  • Mar 19th, 2007
 

10 digit numbers whose sum is 4

1 1 1 1
10*9*8*7/4 = 1260

1 1 2
10*9*8/3 = 240

13
10*9=90

2 2
10*9/2 = 45

4
10

1645

1,1,1,1-> 10*9*8*7/4= 1260
1,1,2   -> 10*9*8/2   =360
1,3      ->10*9      =90
2,2      ->10*9/2   =45
4         ->10          =10

total=1765

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Startin No. = 1 then we have 1,1,1 or  2,1 or just 3 as other digits
which means that for this we have 1*9c3+1*9c2+1*9c1 ways

2. Now other case, starting No. = 2, other digits can be 1,1 or 2
so we have 1*9c2 +1*9c1

3. Starting No. = 3 just 1 digit left i.e. 1
No. of ways== 9c1

4. When stsrting digit = 4 rest all has to be 0 so just 1 way

Adding all those above combinations we have 168 nos.

Cheers

dasbharathi

  • Jan 14th, 2010
 

PRASANNA is right almost except some..
The Correct Answer S =214
Possibilities 
4                       1

3  1                   18      (since 2 digits re diff case I:3 can occupy first place                                           
                                     with combination of 1. case II:1 can do vice versa)

2  2                   9       (since both re same numbers both case means the same
                                    number here)

1 2 1                72      (sure one number has to occupy first place for ten digit number                      
                                     so two times 9c2 since 1 is repeated twice onl single 1 and 2 re taken into 
                                     account for eg 1000000021 is same as 10000000021 )

1 1 1 1            114     (same first digit occupy by any one number so combination  of  remaining 3
                                      numbers is 9c3)
------------------------------------
Total              214

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