Write all possible three digit numbers using the digits 6,0,4,when(1) Repetition of the digits are not allowed(2) Repetition of the digits are allowed

i need it with proper steps

the digits are 6, 0 , 4 and we are writing three digit numbers so 0 can not be at hundreds' digit.

case I : when repetition of the digits are not allowed.

so only 6 and 4 can be placed as hundreds' place.

when 6 is at hundreds' place : 604 and 640

when 4 is at hundreds' place : 406 and 460

thus the possible numbers, when repetition is not allowed:

604, 640, 406 and 460


case II : when repetition is allowed:

so there arise two cases : (i) when all the digits are same (ii) when 2 digits out of three are same

(iii) all the digits are different

(i) when all the digits are same:

666 , 444 

(ii) when 2 digits out of three are same.

(a) when repeating digit is 0.

600 , 400 [since 0 can not be placed as hundreds' digit]

(b) when repeating digit is 6.

660, 664, 606, 646, 466

(c) when repeating digit is 4.

440, 446,404, 464, 644

(iii) it is same as when repetition is not allowed.

thus the possible numbers when repetition is allowed are:

666, 444, 600, 400, 660, 664, 606,646, 466, 440, 446,404, 464, 644, 640, 604, 460, 406

thus total possible numbers are 18.

hope this helps you.

cheers!!

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