Question

The Spanish teacher at South High School wants to arrange 7 students who travelled to Mexico for a yearbook photo.

a. Is this a permutation or combination?

b. How many ways can the students be arranged?

Short answer

a.In the given situation, to arrange the students is a permutation.

b.7 students can be arranged in 5040 different ways.

Step-by-step solution

Part a. Step 1. Define permutation.

When the objects are arranged so that order is important and every possible order of the objects is provided, the arrangements is called a permutation.

Part a. Step 2. Define combination.

A selection of objects in which order is not important is called a combination.

Part a. Step 3. To determine whether, the given statement is a permutation or combination. 

To arrange the students, the order of the students is important.

Hence, to arrange the students is a permutation.

Part b. Step 1. Define permutation.

When the objects are arranged so that order is important and every possible order of the objects is provided, the arrangements is called a permutation.

Part b. Step 2. Determine the number of ways to arrange n objects.

The number of ways to arrange n objects$=n!\mathrm{..........}\left(1\right)$

Part b. Step 3. Determine the number of ways to arrange 7 students.

Substitute$n=7$ in equation (1).

The number of ways to arrange 7 students$=7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$

Hence, 7 students can be arranged in 5040 different ways.