Question

holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the house. if order does not matter, in how many ways can she choose the plants for the front of the house? 7 9 21 36

Explanation:

Step1: Identify the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to be chosen. Here, \(n = 9\) and \(r=7\).

Step2: Use the property \(C(n,r)=C(n,n - r)\)

Since \(C(9,7)=C(9,9 - 7)=C(9,2)\)

Step3: Calculate \(C(9,2)\)

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Answer:

36