Question

There are seven bins in a market and each is filled with a different type of fruit. You're making gift baskets that will hold three fruits apiece. How many ways are there to choose 3 fruits from 7 types of fruit

Answer 1

Combinations

The number of ways to select r things from a total of n things is given by combination formula:

$nCr=\frac{n!}{(n-r)!r!}$  [ n! = n*(n-1)*(n-2)*...*1 ]

Our problem wants us to select 3 fruits from a total of 7 types of fruits. So $n=7$ and $r=3$. Plugging in the formula:

$7C3=\frac{7!}{(7-3)!3!}\\=\frac{7!}{4!3!}\\=35$

So, there are 35 different ways to choose 3 fruits from 7 types of fruit.

ANSWER: 35 Ways

Answer 2

7*6*5*4*3*2*1 / (3*2*1 * 4*3*2*1) = 35

 there are 35 different ways