Question

1. if paul has an apple, an orange, a pear, and a banana at home and he wants to bring two pieces of fruit for lunch, how many different pairs of fruit can he bring to school?

24
6
12
16

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 4, and the order doesn't matter. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 4 \) (total fruits) and \( k = 2 \) (fruits to choose).

Step2: Calculate factorials

First, calculate the factorials: \( 4! = 4\times3\times2\times1 = 24 \), \( 2! = 2\times1 = 2 \), and \( (4 - 2)! = 2! = 2 \).

Step3: Apply the combination formula

Substitute into the formula: \( C(4, 2)=\frac{4!}{2!(4 - 2)!}=\frac{24}{2\times2}=\frac{24}{4} = 6 \).

Answer:

6