Chapter 12: Q3. (page 641)

Determine whether the statement $C (n, r) = P (n, r)$ is sometimes, always, or never true. Explain your reasoning.

Short Answer

Expert verified

The statement istrue when r = 0 or 1.

Step by step solution

Step 1. Given Information.

Given to check whether the statement $C (n, r) = P (n, r)$ is sometimes, always, or never true.

Step 2. Calculation.

When n objects are available and r are to be picked then the number of combinations is given by $C (n, r) = \frac{n!}{(n - r)! r!}$

When n objects are available and r are to be picked then the number of permutations is given by $P (n, r) = \frac{n!}{(n - r)!}$

When $C (n, r) = P (n, r)$ ,

$\begin{array}{l} C (n, r) = P (n, r) \\ \frac{n!}{(n - r)! r!} = \frac{n!}{(n - r)!} \\ \frac{1}{1 r!} = \frac{1}{1} \\ r! = 1 \end{array}$

For the statement to be true, $r! = 1$ i.e., $r = 0 or 1$ .

Step 3. Conclusion.

Therefore, the statement is true when r = 0 or 1.

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Determine whether the statement $C (n, r) = P (n, r)$ is sometimes, always, or never true. Explain your reasoning.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Determine whether the statement Cn,r=Pn,r is sometimes, always, or never true. Explain your reasoning.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Decision Maths

Discrete Mathematics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Determine whether the statement $C (n, r) = P (n, r)$ is sometimes, always, or never true. Explain your reasoning.