how many 5 digit numbers of distinct digits can be formedsuch that the middle place isoccupied by largest number?

       1 1 2 1 1 = 1 way

        x x 3 x x  =  2*3*1*3*3  

        x x 4 x x =    3*4*1*4*4

              and so on

        x  x 9 x x =   8*9*1*9*9

hence total no. of ways =  sigma n from 3 to 9      n^{3 ₍}n-1)   

No more cases possible

Hence, answer = 8 × 8 ×7 × 6 + 7 × 7 × 6 × 5 + 6 × 6 × 5 × 4

+ 5 × 5 × 4 × 3 + 4 × 4 × 3 × 2 + 3 × 3 × 2 × 1