Question

21 multiple choice 2 points
in how many different ways may seven persons be seated in a row of seven chairs?
5,040
10
7
49
22 multiple choice 2 points
each of the following categories describes some data that are to be collected. which of the categories will yield data that are qualitative?

1. the number of children in your house
2. your favorite type of pie
3. your eye color
4. the average time you spend on the phone

1 and 2
2 and 3
1 and 3
3 and 4

Explanation:

Question 21

Step1: Identify the problem type

This is a permutation problem where we want to find the number of ways to arrange 7 people in 7 chairs. The formula for permutations of \( n \) objects taken \( n \) at a time is \( n! \) (n factorial).

Step2: Calculate \( 7! \)

The factorial of a number \( n \) is defined as \( n! = n \times (n - 1) \times (n - 2) \times \dots \times 1 \). So, \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \).
Calculating step by step: \( 7\times6 = 42 \), \( 42\times5 = 210 \), \( 210\times4 = 840 \), \( 840\times3 = 2520 \), \( 2520\times2 = 5040 \), \( 5040\times1 = 5040 \).

Qualitative data is non - numerical, describing characteristics or qualities.

1. "The number of children in your house" is numerical (quantitative).
2. "Your favorite type of pie" describes a quality (qualitative).
3. "Your eye color" describes a quality (qualitative).
4. "The average time you spend on the phone" is numerical (quantitative). So the categories that yield qualitative data are 2 and 3.

Answer:

A. 5,040

Question 22