Question: Evening Out

Comment on Evening Out

Hi Brent

If the order is not important, will the answer be 60/3!= 10
gmat-admin's picture

If by "order isn't important," do you mean that the couple can see a movie first, then visit a teahouse and then go to a restaurant? If so, then the answer is (60)(3!)

For example, in the original question, one outcome might be McDonalds for dinner, then the Matrix for the movie, and then Joe's teahouse.

If order doesn't matter, then the 3 activities in that one outcome can be performed in 3! ways.

Since we can take each of the 60 outcomes and re-order each them in 3! ways, the correct answer (if order doesn't matter) is (60)(3!) = 180

I`m a bit confused. If the order is not important then it is combination and we have to divide by n! which is 3 slots in this case! if we multiply by 3! it is permutation.

What am I missing here?
gmat-admin's picture

Be careful. The "does order matter?" question applies to situations in which we are SELECTING objects from a group of objects.

So, for example, if we want to select 2 students from 5 students, we might ask "Does the order in which I select the two students matter?" Perhaps order does matter. It may be the case that the first student selected will be given one duty, and the second student selected will be given a different duty. If that's the case, we'll use the FCP and see that the number of outcomes = 5 x 4 = 20

If order does NOT matter (for example, perhaps both selected students are given an apple), then we can select 2 students in 5C2 ways (10 ways).

Your new proposed question is about ARRANGING the activities. In your question, you are saying that going to McDonalds for dinner, then the Matrix for the movie, and then Joe's teahouse is DIFFERENT from going to McDonalds for dinner, then going to Joe's teahouse and then the Matrix.

In the original question, the activities/objects are pre-arranged (dinner then movie then tea).

In your question, we must ADD an additional step of ordering the activities in a variety of ways.

Clear!

Many thanks Brent.

Is this a combination problem? 4C1×5C1×3C1
gmat-admin's picture

It's a bit of each, but I'd call it more of a Fundamental Counting Principle (FCP) question.

It just happens to be the case that nC1 always equals 1 (e.g., 4C1 = 4, and 9C1 = 9)
So, we can express our answer as 4 × 5 × 3
Or we can express our answer as 4C1 × 5C1 × 3C1
The final answer is the same.

Cheers,
Brent

Hi Brent, I am trying to understand why we cant apply the MISSISSIPPI rule here? I mean 12!/(4!*5!*3!)? Is that because the 4 restaurants are different from each other as opposed to questions where 4 balls are all identical and RED, where we do use the MISSISSIPI RULE? thanks
gmat-admin's picture

There are two ways in which this question differs from a question that we could solve with the MISSISSIPPI rule:

1) The 4 restaurants are all DIFFERENT, the 5 movies are all different, and the 3 teahouses are all different. The MISSISSIPPI rule applies only to questions in which we have IDENTICAL elements.

2) If we want to apply the MISSISSIPPI rule, we must arrange ALL of the elements in the group. So, for example, in the original MISSISSIPPI question, we want to arrange all 11 letters in a row. In the above question, we are selecting only 3 of the 12 elements.

Does that help?

Cheers,
Brent

thanks

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