If a 4 digit number is formed at random without repetition using the digits 0, 1, 2, 3, 4, then the probability that the number thus formed is even is

If a 4 digit number is formed at random without repetition using the digits 0, 1, 2, 3, 4, then the probability that the number thus formed is even is

There are 4 places: _ _ _ _

As repetition is not allowed,

Thousands place cannot have 0, so there are only 4 choices for that position.

Hundreds place can have all other remaining 4 choices for that position.

Tens place  can have all other remaining 3 choices for that position.

Units places can have only remaining 2 choices

So, through fundamental process of counting

No. of numbers possible = 4 x 4 x3 x 2 =96

For even nos. units place should be either 2 or 4 or 0

In a similar way of counting lets first fix 2 or 4 

So for thousands place 3 options are remaining (except 0).

Hundreds place can have all other remaining 3 choices for that position.

Tens place can have all other remaining 2 choices for that position.

Units places can have only remaining 2 choices. (2 or 4)

No. of numbers possible = 3 x3 x 2 x 2 = 36

In a similar way of counting lets first fix 0

So for thousands place 4 options are remaining (except 0).

Hundreds place can have all other remaining 3 choices for that position.

Tens place can have all other remaining 2 choices for that position.

Units places can have only remaining 1 choices. (only 0)

No. of numbers possible = 4 x 3 x 2 x 1= 24

Total Even nos. 36+24 = 60

Probability = 60/96 = 5/8 Answer