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Chapter 13: Q. 2 (page 854)

True or False $n! = \frac{(n + 1)!}{n}$ .

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step 1. Given infomation.

The given statement is:

$n! = \frac{(n + 1)!}{n}$

02

Step 2. Determine whether the given statement is true or false.

The right-hand side of the equation can be written as:

$\begin{array}{rcl} \frac{(n + 1)!}{n} & = & \frac{(n + 1) \cdot n!}{n} \\ \frac{(n + 1)!}{n} & = & \frac{(n + 1)}{n} \cdot n! \\ \frac{(n + 1)!}{n} & \neq & n! \end{array}$

03

Step 3. Conclusion.

The given statement is false.

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Most popular questions from this chapter

The faculty of the mathematics department at Joliet Junior College is composed of 4 females and 9 males. Of the 4 females, 2 are under age 40, and of the males 3 are under age 40. Find the probability that a randomly selected faculty member is:

(a) Female or under age 40

(b) Male or over age 40

Determine whether the following is a probability model.

In Problems 11–16, construct a probability model for each experiment.

Tossing two fair coins once.

Use the information given in the figure.

How many are in set A?

Use the formula $C (n, r) = \frac{n!}{(n - r)! r!}$ to find the value of each combination.

$C (7, 4)$

See all solutions

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