Question

1. if jackson is at the store and can buy any 3 fruits (the store sells apples, oranges, pears, bananas, strawberries, blueberries, and kiwis), how many different collections of fruit can he choose?

343
35
84
210

Explanation:

Step1: Identify the problem type

This is a combination problem where we want to find the number of ways to choose 3 fruits from 7 types (apples, oranges, pears, bananas, strawberries, blueberries, kiwis). The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n \) is the total number of items, \( k \) is the number of items to choose. Here, \( n = 7 \) and \( k = 3 \).

Step2: Calculate the factorial values

First, find \( n! = 7! = 7\times6\times5\times4\times3\times2\times1 = 5040 \), \( k! = 3! = 3\times2\times1 = 6 \), and \( (n - k)!=(7 - 3)!=4!=4\times3\times2\times1 = 24 \).

Step3: Apply the combination formula

Substitute the values into the formula: \( C(7, 3)=\frac{7!}{3!(7 - 3)!}=\frac{5040}{6\times24}=\frac{5040}{144}=35 \).

Answer:

35 (the option with 35)