Suppose that you go to a local restaurant that is offering a three course meal f

Question

Suppose that you go to a local restaurant that is offering a three course meal for $12.99. Each meal consists of an appetizer, an entree and a dessert. There are 4 appetizers to choose from, 7 entrees to choose from and 3 desserts. Two of the appetizers, three of the entrees and all of the desserts are vegetarian. Given a random three course meal and that all meals are equally likely to be chosen, what is the probability that it is an "all vegetarian" meal (i..e. what is the probability that all three course are vegetarian)? Express your answer as a fraction

Explanation / Answer

no. of ways that anyone can choose vegetarian meal = 2C1*3C1*3C1

no. of ways that random meal is selected =  4C1*7C1*3C1

so probability of vegetarian meal = no. of ways that anyone can choose vegetarian meal /no. of ways that random meal is selected

=2C1*3C1*3C1 /4C1*7C1*3C1

= 2*3*3/4*7*3

=3/14

=0.214

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