Helen wants to buy a bunch of flowers. There are five types of flowers available, namely roses, chrysanthemums, lilies, carnations and tulips. How many possible bunches of 16 flowers can she choose if the bunch must contain no more than two lilies, but any number of the types of flowers.

(a) Let us assume first than no lilies were used 

    Then there are total $= 4^{16}=$ 4294967296 bunches

(b) Let us assume one lily is present

    Total bunches possible $= 4^{15} = 1073741824$

(c)Let us assume two lilies are present

   Total bunches Possible $= 4^{14}$

  Total number of bunches with atmost two lilies-

      $=4^{16}+4^{15}+4^{14}=4^{14}(16+4+1)=21\times 4^{14}=56371445$ 76