A committee of 3 people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
GMAT combinatorics questions get demonized but they are among the most formulaic to tackle. Are there tough ones? Yep. As there are though questions related to any type of GMAT content. But on the whole they're not tougher than anything else and tend to require little calculation. So if you know the system most GMAT combinatorics questions don't take a lot of time or effort. Usually the first thing to think about is whether you're dealing with a group or an order. Are you picking friends to go on vacation with you or are you thinking about how many ways you can line people up? Creating committee's of three people sounds like ordering. There's no spatial element. It's just picking a certain number of people from a larger pool. In this one we're picking three people from a group of 8. However there's a constraint! Always double check for constraints. You don't always have them but often you do. In this case married people can't be together. So you have 8 people but limitations on who can be grouped. Not a big deal. We just have to consider it. Here at Atlantic GMAT we tackle grouping questions as follows:
Define your group: 3
Define your pool: 8
The group defines the number of slots you create. The pool is the number of people that can go into the slots. See digram below and/or check out the video solution: a committee of 3 people is to be chosen from four married
The biggest point of confusion is the denominator. Why is it numbered? Why do we divide? You almost always divide when doing grouping, Why? If you don't then you over-count. Why? Because then you are counting the spatial element. If you don't divide then group A, B, C is also counted as C, B, A and B, C, A, and B, A, C even though those are all the same group. Another way to look at the division is that you're dividing by the number of times that three things can be ordered: 3!. That way you don't count the spatial/ordering. Here are some extra combinatorics questions to practice on: GMAT Question of the day Combinatorics. These are not official GMAT questions and in general are very difficult. That said, there's a lot to learn from them in terms of combinatorics technique. Comment with any questions or additions. Happy studies!