Question

1. if linda is at the store and can buy any two fruits (the store sells apples, oranges, pears, bananas, and kiwis), how many combinations of fruit can she choose?

25
15
3
10

Explanation:

Step1: Identify the problem type

This is a combination problem where we need to find the number of ways to choose 2 fruits from 5 types (apples, oranges, pears, bananas, kiwis). The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 5 \) (total number of fruits) and \( k = 2 \) (number of fruits to choose).

Step2: Calculate factorial values

First, calculate the factorials: \( n!=5!=5\times4\times3\times2\times1 = 120 \), \( k!=2!=2\times1 = 2 \), and \( (n - k)!=(5 - 2)!=3!=3\times2\times1 = 6 \).

Step3: Substitute into the combination formula

Substitute these values into the formula: \( C(5, 2)=\frac{5!}{2!(5 - 2)!}=\frac{120}{2\times6}=\frac{120}{12}=10 \).

Answer:

10