# For dessert you can choose apple, cherry, or peach pie to eat, and milk or juice to drink. How many different combinations can you choose from?

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The answer is that you can choose from 6 possible combinations.

Without doing this mathematically, you can simply look at the fact that you have 3 kinds of pie and 2 kinds of drinks. You can have each kind of pie with each drink. This means that you can have 6 pie and drink combinations.

Depending on what your teacher wants to see, you should probably make a tree diagram to count the possible choices.

Simply list the two drink choices and then, under each, list the three pie choices. You can then find the final result by counting the number of pie choices.

The options you have are:

To eat: Apple pie, Cherry pie, or peach pie = 3 desserts

To drink: milk or juice = 2

Then you can choose one from each:

Then your choices are:

(apple, milk) (apple, juice) (cherry, milk)(cherry, juice) (peach, milk) and (peach, juice)= 6

Then you have 6 different combination to choose from.

A:

The number of possible combinations of having from apple, cherry or peach pie:

zero item : 1 way

1 items : 3 ways

2 items : 3 ways

All 3 items : 1 way.

Total possible combination: 1+3+3+1 = 2^3 =8 which incudes 0 combination or not taking anything also.

B:

The number of combinations possible for milk or tea.

Number of combination of not taking of any thing = 1 possible way.

Number of combinations of not taking only one drink =2 possible ways.

Number of combination of taking both drinks =1

Total possible combinations: 1+2+1= 2^2 =4.

Since A and B are independent events n (A & B) = n(A)*n(B) = 8*4 =32 including not choosing anything.