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A menu has - 6 starters - 10 main dishes - 7 desserts - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Question 13
A menu has - 6 starters - 10 main dishes - 7 desserts. (a) A three-course meal consists of a starter, a main dish and a dessert. How many different three-course m... show full transcript
Worked Solution & Example Answer:A menu has - 6 starters - 10 main dishes - 7 desserts - OCR - GCSE Maths - Question 13 - 2018 - Paper 1
Step 1
How many different three-course meals are possible?
Answer
To determine the number of different three-course meals, we use the multiplication principle of counting. A three-course meal consists of one starter, one main dish, and one dessert. Therefore, the total number of combinations can be calculated by multiplying the number of choices for each course:
Number of three-course meals = Number of starters × Number of main dishes × Number of desserts
Substituting the values:
Number of three-course meals = 6 × 10 × 7 = 420.
Thus, there are 420 different three-course meals possible.
Step 2
Show that there are 172 possible different two-course meals.
Answer
For two-course meals, we have three combinations:
- A starter with a main dish
- A starter with a dessert
- A main dish with a dessert
Now, we will calculate the number of possibilities for each combination:
-
Starter with a main dish: There are 6 choices of starters and 10 choices of main dishes, giving:
Number of combinations = 6 × 10 = 60.
-
Starter with a dessert: Here, we have 6 choices of starters and 7 choices of desserts:
Number of combinations = 6 × 7 = 42.
-
Main dish with a dessert: In this case, we have 10 choices of main dishes and 7 choices of desserts:
Number of combinations = 10 × 7 = 70.
Finally, we add these three quantities together to get the total number of two-course meal combinations:
Total = 60 + 42 + 70 = 172.
Therefore, there are 172 possible different two-course meals.