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Nikumbh • Apr 13, 2012

# Problem in aptitude

In a 6 digit number, find the possibilities of at least 4 digits are different...
It's really needed............
In a 6 digit number, find the possibilities of at least 4 digits are different
means 4 or 5 or 6 digits are different
Case 1:
first take case all 6 digits are different.total 10 digits are there(0,1,2,3,4,5,6,7,8,9)
- - - - - -
in first place we can fill 9 different ways even though if we have 10 digits because in first place if we put 0 it becomes 5 digit number,in second place one of the remaining 9 digits,3rd digit 8 ways 4th digit 7 ways
5th digit 6 ways and 6th digit in5 ways.so total number 6 digit numbers all are different are
9*9*8*7*6*5=136080
Case 2:
in this case 5 digits are different
first form 5 digit number with all are different and remaining 1 palce can be filled by any one of the digit (10C1)
9*9*8*7*6*10=272160
Case 3:
in this 4 digits are different in this again 2 sub cases are there
sub case3.1:
2 in total number 2 digits are same (example 987698)
in this 4 digits are different filled renaming 2 digits can be placed 90 ways.
9*9*8*7*10*9=408240
subcase 3.2:
in this total 6 digits 3 are same like(987699 means in this 9 comes three times)
total=45360
Total Possible numbers are
136080+272160+408240+45360=861840

Once check this answer is correct or not
Nikumbh • Apr 13, 2012
Mr. Naresh Kumar , Thank you very much for your clarification.