Question

You have five different varieties of flowers and you want to put 3 different varieties in each vase how many cases will you make without duplicating a vase

Answer 1

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 $5C3$ ways.

$NCr=\frac{N!}{(n-r)!(r!)}$

$5C3=\frac{5!}{(5-3)!3!} = \frac{5\times 4\times 3\times2\times1}{(2\times1)(3\times2\times1)}=\frac{5\times4}{2\times1}=\frac{20}{2}=10$

Thus, we can make vase in 10 different ways without duplicating a vase.