Question

In a tea shop there are 30 different types of green tea. How many ways can I
select 15 different types of green tea to take home?

Answer 1

Answer: 155117520

Step-by-step explanation:

The number of combinations of r things selected from a group of n things at a time is given by :-

$^nC_r=\dfrac{n!}{(n-r)!r!}$

Given : The total number of different types of green tea = 30

The number of different types of green tea you wish to select =  15

Then , the number of combinations of selecting 15 different types of green tea from 30 at a time is given by :-

$^{30}C_{15}=\dfrac{30!}{(30-15)!15!}\\\\=\dfrac{30!}{15!15!}=155117520$

Hence, there are 15511752 ways you can select 15 different types of green tea to take home.