   Chapter 14.2, Problem 46E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# An unlikely event The president of a large company selects six employees to receive a special bonus. He claims that the six employees are chosen randomly from among the 30 employees, of whom 19 are women and 11 are men. What is the probability that no woman is chosen?

To determine

To find:

The probability that no woman is chosen.

Explanation

Given:

The president of a large company selects six employees to receive a special bonus. He claims that the six employees are chosen randomly from among the 30 employees, of whom 19 are women and 11 are men.

Approach:

Combinations: Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

Formula used:

Cnr=n!r!(nr)!(1)

Here, n is the total number of items and r is the number of items being chosen at a time.

If E is the event in a sample space S, then the probability of E is

P(E)=n(E)n(S)(2)

Calculation:

There are 30 employees in company. So,

n=30

Six employees are selected at random. So, the number of possible outcomes is,

n(S)=C306

Substitute 30 for n and 6 for r in equation (1).

C306=30!6!(306)!=30!6!24!

Now,

n(S)=30!6!24!

There are 19 are women and 11 are men

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