Question

when you calculate the number of combinations of r objects taken from a group of n objects what are you counting? give an example.
choose the correct answer below.
a. you are counting the number of ways to select r of the n objects without regard to order. an example of a combination is the number of ways a group of teams can be selected for a tournament.
b. you are counting the number of ways to select r of the n objects without regard to order. an example of a combination is the number of ways a group of people can be assigned to seats in the front row of a theater.
c. you are counting the number of ways to select r of the n objects with regard to order. an example of a combination is the number of ways a group of teams can be selected for a tournament.
d. you are counting the number of ways to select r of the n objects with regard to order. an example of a combination is the number of ways a group of people can be assigned to seats in the front row of a theater.

Explanation:

Step1: Recall combination and permutation concepts

Combination is selection of \(r\) objects from \(n\) objects without regard to order, and permutation is selection with regard to order.

Step2: Analyze options

• Option A: Selecting \(r\) teams out of \(n\) teams for a tournament without regard to order is a combination problem.
• Option B: Assigning \(r\) people to \(r\) seats in a theater (order of seating matters) is a permutation problem.
• Option C: Selecting \(r\) teams out of \(n\) teams with regard to order is a permutation problem.
• Option D: Assigning \(r\) people to \(r\) seats in the front - row of a theater (order of seating matters) is a permutation problem.

Answer:

A. Selecting a group of teams for a tournament without regard to order is an example of a combination.