The number of natural numbers less than 1000 in which no two digits are repeated is 

  Number of single digit numbers  =  $-\to 9$   ( except 0)  

  Number of two digit numbers        =   $--\to 9\times 9=81$    ( tenth place can be filled in 9 ways( except 0) and unit's place can be filled in 9ways

   Number of three digit numbers     =   $---\to 9\times {}^{9}P_2=648$  ( hundred's placed can be filled in 9 ways ( except 0) and the remaining two

                                                                                                        places can be filled with the remaining 9 numbers in P(9,2) ways.       

The number of natural numbers less than 1000 in which no two digits are repeated is  $=738$