Five students and two teachers attend a conference at Statistics Canada. They pose for a picture. In how many ways can they line up, side by side, for a picture? In how many ways can they line up if they must have the teachers on both sides of the picture? What is the probability that the two teachers occupy two of the three middle slots?

480 ways

240 ways

Probability = 1/7

Step-by-step explanation:

Given:

Number of student = 5

Number of teacher = 2

Computation:

1. Number of ways can they line up, side by side, for a picture.

5! × 2! × 2

480 ways

2. Number of ways can they line up if they must have the teachers on both sides of the picture.

5! × 2!

240 ways

3. Probability that the two teachers occupy two of the three middle slots.

³C₂ × 5! × 2!

720 ways

Total number = 7! = 5,040 ways

Probability = 720 / 5,040

Probability = 1/7