Question

How many five digit even numbers can be formed by using the digits $0,2,3,4,5$ (Rept. not allowed)?

Answer 1

1. At first digit we can put any number except $0$

So, first digit can be filled with $4$ ways (2,3,4,5 can only be used)

2. At second digit we can put any number out of remaining numbers (as 1 is used at first digit place)

So, it can be filled with $4$ ways

3. At third digit we can put any number out of remaining numbers (as of now 2 digits has been used)

So, it can be filled with $3$ ways

4.At fourth digit we can put any number out of remaining numbers (as of now 3 digits has been used)

So, it can be filled with $2$ ways

5. Similarly , fifth digit can be filled with $1$ way

therefore, Total digits formed $=4\ast 4\ast 3\ast 2\ast 1=96$