How many four digited numbers can be formed using the digits 1,2,5,7,8,9 ?
How many of them begin with 9 and end with 2 ?

Explanation

The number of four digited numbers that can be formed using the given digits 1,2,5,7,8,9 is `""^(6)P_(4)=360`. Now, the first place and last place can be filled with 9 and 2 in one way.
`9 square square 2`
The remaining 2 places can be filled by the remaining 4 digits 1,5,7,8. Therefore these two places can be filled in `""^(4)P_(2)` ways. Hence, the required number of ways `=1. ""^(4)P_(2)=12`.