If you plug 3^10 into a calculator, the answer is 59049. Some of these guesses weren't even close lol
which means there are 3^32 possibilities for the T5 builds which was the point of making the thread.
Killa, there are multiple ways to do this problem.. Depending in the statistics chapter depends on the way you do the problem. You can use 10 choose 3 on the calculator and obtain that answer or do it the way I stated earlier.
I think there would be 64. Say you have all volleyball captains. That's one. Now you remove one at a time for an exchange student. That's 32 more. Now you can replace those exchange students with lab geeks one by one. That's 32 more. Wait that's 65... No?
Im certain now It's not 3^32 for t5 builds... 31 volleyball captains and one lab geek will give the same as 30 volleyball captains and 2 exchange students I think.
I just checked and lab geek is 1:6 exchange is even and volleyball is 6:1. There would be 3^32 different ways to full your crew, but several of them would give the same kcs result. There are not 3^32 different t5 builds.
Because of that ratio it would actually have to be 27 volleyballs and 5 exchange students to equal 31 volleyball and one lab geek. I just thought about a much easier example though lol, which is how many ways there are to have even stats alone. You could have 32 exchange students, 10 exchange 11 volleyball 11 lab geek, 16 volleyball 16 lab geek etc. these are all different dorm make ups but they're all an even build. Because of that I know that there are not 3^32 t5 builds. Ill be done spamming this thread until somebody else posts
there are 3^32 different ways to do the builds lets put it at that so it is easier to understand what I was talking about
Different ways to fill your dorms yes... If you're looking at which dorm they're in. There's also like 50 ways to have 16 volleyball captains and 16 lab geeks so even then...
In the White House question, the position matters because the positions are all different. If the position matters here then it still holds true that there are 3^32 ways to arrange tier 5 crew into 32 dorms. This is known as a permutation. If the order does not matter then it is a combination which will have a different result.
Killenem. Regarding your first post... 10 choose 3 = 120. So I dunno why you said 10 choose 3 and then say 1000 and 720 since neither of those = 120. Also, you have the meaning of "probability" wrong. When you say "the probability the first gets it is 10" that literally means "the chance that the first gets it is 1000%" since probability is a percent and probability is between 0 and 1 for any real life scenario and refers to the liklihood of an event occuring and NOT the total number of different scenarios. You also started off by saying "the probability of given 10 choose 3..." which is also wrong to say because 10 choose 3 doesn't give you a probability, it gives you the total number of combinations of how many groups of 3 you can make when you have 10 items. And you also got it backwards when you said 1000 and 720. You imagined it like there are 3 seats and you have 10 different people that you can put in each seat. This would give 10 choices for the first seat, 9 choices for the second seat, and 8 choices for the third seat. Of if order doesn't mater then it's 10 people that could sit in any seat so 3^10. Therefore you worked it backwards since instead of 3 seats for 10 people, there are 10 seats for 3 people.
Clearly the order shouldn't matter for dorms so it would be a combination involving the choose function. For example, putting a volleyball player in the second dorm and an exchange student in the third dorm should be considered the same as putting a volleyball player in the third dorm and an exchange student in the second. As far as the amount of total different builds you can make with T5, I dunno. There are a ton that are similar because you can alternate one-sided crew which is the same as putting in crew of equality so I do not know how much you would have to divide by to consider the over counting...
I thought 64 at first but I got 65... 32 volleyball guys is one and then all the way to 32 exchange and 32 lab geeks is 64 more. I explained that in one of my other posts lol. 65 just isn't a nice even number... I'd have trouble saying 65 instead of 64.