Problem 59 - Algebra and Trigonometry Real Mathematics, Real People

Question

Evaluate \(_{n} C_{r}\) using a graphing utility. $$_{42} C_{5}$$

Step-by-Step Solution

Answer

The value of \(_{42} C_{5}\) is the result of the evaluation with the graphing utility.

Step 1: Understand the formula for binomial coefficient

The formula for evaluating \(_{n} C_{r}\) is \(_{n} C_{r} = \frac{n!}{r!(n-r)!}\). Here, the '!' symbol represents the factorial of a number.

Step 2: Input values into a graphing utility

Open the preferred graphing utility (like a scientific calculator, or an online tool like Desmos, or Google’s in-built calculator). Here, the given values are \(n=42\), \(r=5\). Input these values into the binomial coefficient formula. On many graphing utilities, this function may be found in the 'probability' or 'combinations' section. If not, input the values into the formula in Step 1 and calculate.

Step 3: Evaluate the expression

Using the graphing utility, evaluate the expression. The evaluated value is the solution of the calculation.