I am unable to understand the solution for this question. In the solution video Greg says that, you can ignore freshmen and sophomores so only group we need to care about is the juniors and seniors and since all 3 juniors must come before first senior we will have 3/6 possibilities for the first position followed by 2/5 followed by 1/4 and then the other three blanks would be 1,1,1. Now my problem with this approach is, it is not very intuitive like if this were to appear on GRE would have started by making cases which is tedious but I am also not able to get all the cases so that it adds up to 1/20. How do we identify such tricks?
How do we now in this case our answer won’t get affected if we ignore freshmen and sophomores?
I believe ignoring the freshman and sophomores is alright in this case because we don’t care when they are picked to meet. Their order doesn’t affect the outcome we are interested in which is the order of all juniors and seniors.
if you imagine a scenario using F, S, Jr, Sr, we could have F F F S S S {Jr, Sr, Jr, Jr, Sr, Sr}. See how the freshman and sophomores didn’t matter?
You can insert any of the Freshman (F) or Sophomore (S) anywhere within the {} brackets in the example above without it impacting what we care about: whether all juniors came before all seniors (in this case, no).
Once we realize this we can move on and think of the problem like the simple example of picking balls out of a bag. We have a bag with 6 balls, 3 Jr, 3 Sr. Then we just need to get three juniors in a row, and the last 3 picks will be seniors: thus, Greg’s solution
