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12 February, 10:39

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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  1. 12 February, 10:50
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    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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