Answer:
10
Step-by-step explanation:
Given:
There are 5 different varieties of flowers.
To place 3 different varies in each vase.
To find how many ways we can do so without duplicating a vase.
Solution:
We need to choose 3 different flowers out of 5 different variety of flowers.
In order to do so we use combination.
We can place the flowers in [tex]5C3[/tex] ways.
[tex]NCr=\frac{N!}{(n-r)!(r!)}[/tex]
[tex]5C3=\frac{5!}{(5-3)!3!} = \frac{5\times 4\times 3\times2\times1}{(2\times1)(3\times2\times1)}=\frac{5\times4}{2\times1}=\frac{20}{2}=10[/tex]
Thus, we can make vase in 10 different ways without duplicating a vase.
