Question

A catering service offers 5 appetizers, 7 main courses, and 10 desserts. A customer is to select 3 appetizers, 2 main courses, and 2 desserts for a banquet. In how many ways can this be done?

Answer 1

9450 different ways

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This problem can be solved using the concept of combinations.

Use the combination formula:

• C(n, k) = n! / (k!(n-k)!), where 'n' is the number of options, and 'k' is the number of selections to be made

For the appetizers,

• C(5, 3) = 5! / (3! (5-3)!) = 10 ways

For the main courses,

• C(7, 2) = 7! / (2! (7-2)!) = 21 ways

And for the desserts,

• C(10, 2) = 10! / (2 (10-2)!) = 45 ways

Since these are independent events, we multiply the total ways together:

• 10 * 21 * 45 = 9450 different possible combinations of selections