Case I The number of ways to form four digit integers =3×3×2×1=18 (first place can be filled by one of the three choices 1,2,3) Case II The number of 3 -digit integers =3×3×2=18 Case III The number of 2 -digit integers =3×3=9 Case IV The number of 1 -digit integer =3 ∴ The number of distinct positive integers =18+18+9+3=48