6. How many 3-digit odd numbers can be formed from the digits 1,2,3,4,5,6 if:

(a) the digits can be repeated (b) the digits cannot be repeated?

Number of places [(x), (y) and (z)] for them = 3

Repetition is allowed and the 3-digit numbers formed are odd

Number of ways in which box (x) can be filled = 3 (by 1, 3 or 5 as the numbers formed are to be odd)

               m = 3
Number of ways of filling box (y) = 6                           (∴ Repetition is allowed)

               n = 6

Number of ways of filling box (z) = 6                           (∵ Repetition is allowed) 

              p = 6

∴  Total number of 3-digit odd numbers formed

                             = m x n x p = 3 x 6 x 6 = 108

(b) Number of ways of filling box (x) = 3                     (only odd numbers are to be in this box )  

                                   m = 3

Number of ways of filling box (y) = 5                                (∵ Repetition is not allowed)

                              n = 5

Number of ways of filling box (z) = 4                                 (∵ Repetition is not allowed)

                             p = 4

∴     Total number of 3-digit odd numbers formed

                                  = m x n x p = 3 x 5 x 4 = 60.