There is nothing wrong with using the word "arrangements" to conclude that the first is a permutations question and using the word "groups" to conclude that the second is a combinations question.
Permutations yield more results than combinations precisely because we care about the arrangements and aren't satisfied to just know the group of people selected.
In this case, for every 1 group of people (Al, Bob, Carl), there will be 6 arrangements possible: ABC, ACB, BAC, BCA, CAB, CBA. So, the answer to #1 will be 6 times the answer to #2.
To actually answer them:
1. There are 7 choices for seat 1, then 6 choices for seat 2, then 5 choices for seat 3. 7*6*5 = 210.
2. 7 choose 3 = 7!/(3!4!) = (7*6*5*4*3*2*1)/(3*2*1*4*3*2*1) = (7*6*5*4*3*2*1)/(3*2*1*4*3*2*1)
= (7*6*5)/(3*2*1) = (7*6*5)/(6) = (7*5)/(1) = 35.
Let me know what you think.
Greg Michnikov, Founder of GMAT Boost
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