Question

question 4 (1 point)
you are eating a 6 course meal how many options are there if:
the dessert must be last and the appetizer must be first 2 marks

your answer:

question 5 (1 point)
you and your 4 friends are playing with a parachute. (you hold a parachute in a circle).
a) how many arrangements can be made?

your answer:

Explanation:

Fix the positions of the first and last courses

We have a 6-course meal.
The first course must be the appetizer (1 option).
The last course must be the dessert (1 option).
Using the Permutations with Constraints knowledge point:

$$ \text{Appetizer} = \text{Position 1} $$

$$ \text{Dessert} = \text{Position 6} $$

Arrange the remaining middle courses

There are 4 remaining courses to arrange in the 4 middle positions.
The number of ways to arrange these is:

$$ 4! = 4 \times 3 \times 2 \times 1 = 24 $$

Determine total arrangements for Question 4

Multiply the options for each position:

$$ 1 \times 24 \times 1 = 24 $$

Calculate circular arrangements for Question 5

There are 5 people (you and 4 friends) standing in a circle.
For circular permutations of \(n\) distinct objects, the number of arrangements is:

$$ (n - 1)! $$

For \(n = 5\):

$$ (5 - 1)! = 4! = 24 $$

Answer:

Question 4

24

Question 5

24