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Chapter 9: Problem 59

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

Short Answer

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

Step by step solution

01

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.
02

Input values into a graphing utility

Open the preferred graphing utility (like a scientific calculator, or an online tool like Desmos, or Google鈥檚 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.
03

Evaluate the expression

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

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Most popular questions from this chapter

Find the binomial coefficient. \(_{14} C_{1}\)

A hardware store makes a profit of \(\$ 30,000\) during its first year. The store owner sets a goal of increasing profits by 5000 dollar each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

Find the indicated term of the sequence. $$\begin{aligned} &a_{n}=\frac{2^{n+1}}{2^{n}+1}\\\ &a_{7}= \end{aligned}$$

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