Maya A.

# Solving word problems

Ahmad is on a Facebook group that has 7 members. How many different sub groups of 3 people could be formed that have Ahmad as a members?

## 2 Answers By Expert Tutors

By:

Diane S.

tutor
Thank you Thomas. This answer is corrected below. My answer inlcludes ALL groups of 3. They want Ahmad included in the chosen group!  My bad. I did not read the question carefully enough.  I apologized that I rushed and missed the actual question. Thanks Thomas. (See below).

If the questioner is interested in how to apply the thinking above to the problem -- Ahmad is included in the chosen three so in reality we are only picking TWO other people. You have only 6 members left to pick from for the first slot, because you have already chosen Ahmad. Then 5 for the second. 6x5 =30 ways to pick 2 remaining people. But again you have overcounted - you can pick me then you, or you then me - and wind up with the same group. so how many ways can you pick 2 people?  You have 2 choices for the first pick and 1 choice for the second pick. 2x1 is 2.  So I have to take my total, 30, and divide by my overcounting of each subgroup, 30/2= 15.
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04/30/18

Thomas R. answered • 04/30/18

Tutor
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Over 25 years of experience and a sense of humor about math

Diane S.

tutor
Thanks Thomas. And I apologize to the questioner. I read too fast and missed that Ahmad was in the group. I corrected it above. I take the long way rather than use combinations and permutations as I find if students don't have a feel for the vocabulary and thinking behind the calculations, they have a hard time remembering the formulas long term and applying them correctly. thank you for your correction and explanation.
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04/30/18

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