Question

7. There are seven clarinet players in the concert band. In how

many ways can they be seated in seven chairs at a concert?
Use the Fundamental Counting Principle.
A. 5,040
C. 840
B. 2,520
D. 210​

Answer 1

Explanation:

The number of people in the cabinet is 7.

n = 7.

Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.

now using fundamental Counting Principle.

since 7 players can sit on chair in

7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in

7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5,040 ways.

To arrange this seven people in a straight cabinet, the number of way to arrange them is n!

Then,

n! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

There are 5040 ways of arranging them.

Option A is correct.