There is something wrong. The answer is C. May someone check pls ?

Since the resulting number must be EVEN, let's consider two possible cases:

case i: The unit's digit is 0
case ii: The unit's digit is 2 or 6

Question: Why am I considering those two cases separately?
Answer: I'm doing so because we DON'T get a 5-digit number if the first digit is 0 (e.g., 02631 is not a 5-digit number)

case i: The unit's digit (aka the 5th digit) is 0
So, there is 1 way to assign a value to the 5th digit.
There are now 4 digits remaining to choose from.
So, we can assign a value to the 1st digit in 4 ways.
We can assign a value to the 2nd digit in 3 ways.
We can assign a value to the 3rd digit in 2 ways.
We can assign a value to the 4th digit in 1 way.
By the Fundamental Counting Principal (FCP), we can complete all five steps (and create a 5 digit number) in (1)(4)(3)(2)(1) ways (= 24 ways)


case ii: The unit's digit is 2 or 6
Since the last digit is 2 or 6, there are 2 ways to assign a value to the last (5th) digit.
There are now 4 digits remaining to choose from, but one of those values is 0, which we can't choose for the 1st digit.
So, we can assign a value to the 1st digit in 3 ways.

At this point, we can assign any of the remaining three digits to the 2nd, 3rd and 4th places.
So, we can assign a value to the 2nd digit in 3 ways.
We can assign a value to the 3rd digit in 2 ways.
We can assign a value to the 4th digit in 1 way.
By the Fundamental Counting Principal (FCP), we can complete all five steps (and create a 5 digit number) in (2)(3)(3)(2)(1) ways (= 36 ways)

Total number of outcomes = 24 + 36 = 60

Answer: D

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Thank you Sir

Using FCP
I. Last digit: 0
Then by FCP, 4x3x2x1=24
II. Last digit: 2
By FCP: 3x3x2x1= 18
III. Last digit: 2
By FCP: 3x3x2x1= 18
SUM OF ABOVE= 24+18+18= 60
Ans: D

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