The whole family plan went out to dinner. The menu was as follows:. Frst course

Question

The whole family plan went out to dinner. The menu was as follows:.
Frst course chicken vegetable soup; shrimp cocktail fruit salad
Second course: shrimp; vegetable casserole; beef; chicken
Third course: apple pie ;carrot cake; ice cream
Papa wants everyone to order a different meal. (Note that soup beef and pie would be different from soup beef and cake.)Papa wants to know if there are enough different meals available that consists of one item from each course. However he does not want any of the meals to include the same kind of food more than one during the meal. For example if Ed ordered shrimp cocktail then he could not order shrimp for the second course. You may assume that the items containing vegetables contain carrots and that the fruit salad contains apples. How many such meals are possible?

Explanation / Answer

The first course items are chicken, vegetable soup, shrimp cocktail and fruit salad. Thus there are 4 choices

The second course items are shrimp, vegetable casserole, beef , chicken. For each of the 4 first course items there are 4 choices. However, three of these are made up of the same item as three in the first list. So the total number of two meals is 4*4 - 3 = 13.

The third course items are apple pie, carrot cake and ice cream. Apple pie and fruit salad have the same item. Since fruit was not in the first course, it was in 4 two course meals. So there are 4 three course meals that have two apple items. Carrot cake has the same item as vegetable soup which was paired with three second course items. So there are 3 three course items that have both carrot cake and vegetable soup.

Thus the total number of three course meals = 13*4 - 4 -3 = 45.

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