advita wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number?
How many of these are even and how many odd?
pl explain.
How many 3 digit numbers can be formed :
Hundred digit -> 5 ways (you can't put 0)
Tens digit -> 5 ways (all but what we put at hundred's place)
Unit digit -> 4 ways (all but what we put at hundred and unit place)
So, total no. of ways = 5*5*4 = 100
How many odd 3 digit numbers can be formed :
Unit digit -> 3 ways (1,3,5)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
So, total no. of ways = 3*4*4 = 48
How many even 3 digit numbers can be formed :
Even numbers = Total - odd numbers = 100 - 48 = 52
OR (Go through this just for learning)
Two cases:
(unit digit is 2 or 4):
Unit digit -> 2 ways (2,4)
Hundred digit -> 4 ways (all but what we put at unit's place and 0)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 4*4*2 = 32
(unit digit is 0):
Unit digit -> 1 way (0)
Hundred digit -> 5 ways (as 0 is already selected, choose anything)
Ten's digit -> 4 ways (all but what we put at hundred and unit place)
No. of ways = 1*5*4 = 20
Total No. of ways = 32+20 = 52
Note : You can't say that there will be 50% of even numbers and 50% of odd numbers, as because of 0, it is not symmetric. If it would have been any other distinct even number in place of 0, then you can take 50% even and 50% odd numbers. 0 adds a restriction for the hundred's place which other digit don't. So in this case, number of odd numbers are at disadvantage hence would be less than no. of even numbers.
