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?

Respuesta :

Answer:

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

The number of ways that can  they line up, side by side, for a picture is 480 ways

The number of ways can they line up if they must have the teachers on both sides of the picture is 240 ways

Th  probability that the two teachers occupy two of the three middle slots is 1/7

Calculation of number of ways and probability:

Sincee Five students and two teachers attend a conference at Statistics Canada

The number of ways should be

= 5! × 2! × 2

= 480 ways

Now the number of ways is

= 5! × 2!

= 240 ways

Now the probability is

= ³C₂ × 5! × 2!

= 720 ways

And, finally

Total number = 7! = 5,040 ways

Probability = 720 / 5,040

Probability = 1/7

learn more about probability here: https://brainly.com/question/23270719