A catering service offers 7 appetizers, 3 main courses, and 5 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts

Question

A catering service offers 7 appetizers, 3 main courses, and 5 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts for a banquet. In how many ways can this be done?

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Answers ( No )

    0
    2021-09-09T18:37:51+00:00

    This question is based on combinations

    Out of 7 appetizers, 4 are to be selected, this becomes = 7C4

    Out of 3 main courses, 2 are to be selected , this is = 3C2

    Out of 5 desserts, 4 are to be selected, this is = 5C4

    So, total ways become =

    7C4 * 3C2 * 5C4

    7!/4!(7-4)! * 3!/2!(3-2)! * 5!/4!(5-4)!

    = 35*3*5 =525 ways

    Hence, this can be done in 525 ways.

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