PS - Probability

[f2001290]

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?

I am getting even and odd numbers as 52 and 48.
But this is not the OA.

[Neo2000]

To create 3 digit numbers

The first place can be filled in 5ways only (from 1,2,3,4 or 5 let's say 5)
The second place can be filled in 5ways (from 0,1,2,3 or 4 let's say 1)
The third place can be filled in 4 ways ( from 0,2,3 or 4)
So total number of ways of creating 3digit numbers without repetition = 5x5x4 = 100

Exactly half of this will be Odd and half will be Even

[f2001290]

Neo

first part is right, but the OA of second part is 60 and 40.

[Neo2000]

My bad

To Create 3 digit odd numbers
The last place can be filled in 3 ways 1,3,5 lets say 1

The first place can be filled in 4
The second place can be filled in 4ways
So total = 4x4x3 = 48

Which means there are 52 Even numbers

[jayhawk2001]

There are 6P3 - 5P2 numbers in all = 120 - 20 = 100 numbers.

Of this 4*4*3 = 48 are odd and 52 are even (same approach as Neo's)