Question

You have a set of 9 different flowers. How many ways can you arrange them in a vase

if:
a) There are no restrictions.
b) Two specific flowers must always be together?

Answer 1

a) 362880

b) 80640

Explanation:

this is a pretty simple combinatorics problem. we use the factorial to solve these.

first, we can visualize what the problems are

a) _ _ _ _ _ _ _ _ _

the spot here has 9 possibilities, and the next has 8, and so on. we have 9! = 362880 ways.

b) (_ _) _ _ _ _ _ _ _

so now two flowers must always be next to each other. they can act as one whole object, so now we are arranging 8 objects and 2 more inside the brackets.

this is 8!×2! = 80640 ways