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# Problem in aptitude

In a 6 digit number, find the possibilities of at least 4 digits are different...

It's really needed............

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.

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

Once check this answer is correct or not

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**=408240subcase 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

Mr. Naresh Kumar , Thank you very much for your clarification.