A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert. There are 4 different starters, 6 different main courses and 8 different desserts to choose from. (i) How many different three-course meal combinations are available? (ii) When Jack visits the restaurant he discovers that the restaurant still has the 4 starters and the 6 main courses available but is sold out of some of the desserts. Jack now has 120 different three-course meal combinations to choose from. How many different desserts are still available to Jack?

Leaving Cert Mathematics Counting/Permutations: A restaurant is offering a three

A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert - Leaving Cert Mathematics - Question 1 - 2020

Question 1

A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert. There are 4 different starters, 6 different main courses and... show full transcript

Worked Solution & Example Answer:A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert - Leaving Cert Mathematics - Question 1 - 2020

Step 1

How many different three-course meal combinations are available?

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Answer

To find the total number of three-course meal combinations, we multiply the number of choices for each course together:

Number of starters = 4
Number of main courses = 6
Number of desserts = 8

Thus, the total combinations can be calculated as:

ext{Total Combinations} = ext{Starters} imes ext{Main Courses} imes ext{Desserts} = 4 imes 6 imes 8 = 192

Therefore, there are 192 different three-course meal combinations available.

Step 2

How many different desserts are still available to Jack?

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Answer

From the information, we know:

Jack has 4 starters and 6 main courses available.
The total combinations Jack has is 120.

The formula for the number of combinations is:

ext{Total Combinations} = ext{Starters} imes ext{Main Courses} imes ext{Desserts}

Given:

120 = 4 imes 6 imes x

Where $x$ is the number of available desserts. Solving this for $x$ gives:

4 imes 6 = 24

Thus,

120 = 24 imes x \ \Rightarrow x = \frac{120}{24} = 5

Therefore, there are 5 desserts still available to Jack.

A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert - Leaving Cert Mathematics - Question 1 - 2020

Worked Solution & Example Answer:A restaurant is offering a three-course meal consisting of one starter, one main course and one dessert - Leaving Cert Mathematics - Question 1 - 2020

How many different three-course meal combinations are available?

How many different desserts are still available to Jack?

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