Question

Addison decides to Jake 3 different fruits with her toschool today. She has 7 to pick from: grapes, strawberries, akiwi, blueberries, an orange, a peach, and a pear. How manydifferent combinations of 3 fruits can she take?

Answer 1

This is a question asking you to pick 3 fruits from an array of 7 different fruits.

This means we can use combination to solve this question.

To pick r things from a set of n things:

`\begin{gathered} C^n_r=(n!)/(r!(n-r)!) \\ \text{where n! = n }*\text{ (n-1) }*\text{ (n-2) }*\ldots \end{gathered}`

Thus, to pick 3 fruits from a set of 7 fruits:

`C^7_3=(7!)/(3!(7-3)!)=(7!)/(3!4!)=7*5=35`

Therefore, the number of ways to pick 3 fruits from 7 fruits is = 35 ways