Hi All,
We're told in a class of 10 students, a group of 4 will be selected for a trip. We're asked for the number of different groups that are possible, if 2 of those 10 students are a married couple and will only travel together. Since we're dealing with groups, we'll use the Combination Formula (a couple of times) to answer this question.
Given the 'restriction' in the prompt (about the married couple), there are 2 types of groups to consider:
1) Groups WITH the married couple
2) Groups WITHOUT the married couple
WITH the married couple, there will be 2 'spots' for the remaining 8 people, so there are 8c2 = 8!/6!2! = 28 different groups
WITHOUT the married couple, there will be 4 'spots' for the remaining 8 people, so there are 8c4 = 8!/4!4! = 70 different groups
Total possible groups = 28+70 = 98
Final Answer:
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Rich
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