you would like to create a flower arrangement for a friend using flowers from your yard. you have 4 tulips, 10 lantana, 11 zinnias, 14 rain lilies and 12 prickly pear. your vase has room for 6 flowers. you may leave your answer in factorials.

how many different arrangements of your flowers can be made in the vase if you remember that your friend is allergic to tulips and you leave those out? (assume we're interested in the "pile" of flowers not the actual visual order of the flowers).