Explanation Given info: There are 6 snacks and 5 vegetables available in the menu. Calculation: Combinations: A combination is an arrangement of n objects in r ways where the order of arrangement is not considered. n C r = n ! ( n − r ) ! r ! Where, n is the total number of objects and r is number of ways in which n objects can be selected. The number of ways to select 3 snacks out of 6 snacks, Substitute n as 6 and r as 3. 6 C 3 = 6 ! ( 6 − 3 ) ! 3 ! = 6 × 5 × 4 × 3 ! 3 ! 3 ! = 120 6 = 20 Thus, there are 20 ways to select 3 1 st snacks out of 6 snacks. The number of ways to select 2 vegetables out of 5 vegetables, Substitute n as 5 and r as 2

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Chapter 4.4, Problem 63E

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The number ways to select 3 snacks and 2 vegetables.

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Chapter 4.4, Problem 62E

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The number ways to select 3 snacks and 2 vegetables.

Solution Summary: The author explains that there are 200 ways to select 3 snacks and 2 vegetables. Combinations are an arrangement of n objects in r ways.

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