Sara has a white, a pink, a blue, a yellow and an orange flower. Sara has a white, a pink, a blue, a yellow and an orange flower.
She wants to plant these $5$ flowers in a row, but she does not want the orange flower to be the first
or the last flower in the row.
How many different arrangements are possible?
There are three positions in which to place the orange flower (the middle three): that gives $3$ ways to plant that flower. The remaining four spots can be filled in $4!$ ways: That gives us, in total: $$3\times 4! = 3 \cdot (4 \cdot 3\cdot 2\cdot 1) = 72$$ arrangements in which to plant the flowers.
My answer is $3\times 2\times 1$ which is $6$.