Problem 58 - Algebra and Trigonometry Real Mathematics, Real People

Question

Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{10} C_{7}$$

Step-by-Step Solution

Answer

The value of \(_{10} C_{7}\) computed using a graphing utility is 120. It means there are 120 ways to choose 7 items from a group of 10.

Step 1: Open the Graphing Utility

The graphing utility or calculator that will be used here should have the function for calculating combinations. Open the graphing utility to start the calculation process.

Step 2: Input the Combination

There should be an option to input the combination. The specific method of input may vary depending on the graphing utility being used. It could simply have a combination function where the inputs \(_{n} C_{r}\) are \(n = 10\) and \(r = 7\). The input would then look like this: \(_{10} C_{7}\).

Step 3: Evaluate the Combination

After inputting \(_{10} C_{7}\), evaluate, or in other words calculate, the result by pressing the appropriate button in your graphing utility. The utility will perform the calculation using the combination formula \(_{n} C_{r} = \frac{n!}{r!(n-r)!}\), where \(n!\) is the factorial of \(n\), \(r!\) is the factorial of \(r\), and \((n-r)!\) is the factorial of \((n-r)\). The factorial of a number is the product of all positive integers up to that number.

Step 4: Interpret the Result

The output represents the number of ways you can choose 7 items from a group of 10. Note this down.