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Ideal Lineup (Based on everything up to now)

colton said:
Oh, you want to make things complicated, do you?

I'm up for the challenge. Let's say the Jazz have 3 PG (Harris, Tinsley, Watson), 5 "Wings" (Bell, Burks, Hayward, Howard, and Miles), and 5 "Bigs" (Evans, Favors, Jefferson, Kanter, and Millsap), and that Corbin has to pick 1 PG, 2 Wings, and 2 Bigs for each lineup.

In that case, he has exactly 300 different lineups he can choose from. ( 300 = (3 choose 1) * (5 choose 2) * (5 choose 2) , where "a choose b" = a!/(b!(a-b)!) )

One could make things even more complicated, by saying for example Evans can play SF or PF, but not SG or C. In that case you get only 210 different lineups. (Not going to show work for this one unless anyone really cares.)

Boo-yah!
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Wow! That's impressive! Is that from statistics class? Where does one learn such a formula? :)
 
Guitaro said:
Wow! That's impressive! Is that from statistics class? Where does one learn such a formula? :)
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The "a choose b" formula is well known, I think I learned it in high school. My 10th grade daughter certainly knows it, at any rate. The "a choose b" formula tells you if you have a different things, how many different groups of size b you can make. So it's clear that there are, for example, 10 different wing combinations that can be made with 5 different guys playing the two positions (5 choose 2).

Beyond that, it's just figuring out the right way to think of things. In this case, I realized that if there are 3 different PGs, and each PG can work with 10 different wing lineups, then there are 30 PG-wing combinations. And each of those 30 different PG-wing combinations can work with 10 different big combinations, so there must be 300 total different lineups.

So, while it's true I have had a lot of higher math (B.S. degrees in both physics and math, followed by M.S. and Ph.D. degrees in Physics), the hard thing for this particular calculation was just figuring out what needed to be done.
 
colton said:
The "a choose b" formula is well known, I think I learned it in high school. My 10th grade daughter certainly knows it, at any rate. The "a choose b" formula tells you if you have a different things, how many different groups of size b you can make. So it's clear that there are, for example, 10 different wing combinations that can be made with 5 different guys playing the two positions (5 choose 2).

Beyond that, it's just figuring out the right way to think of things. In this case, I realized that if there are 3 different PGs, and each PG can work with 10 different wing lineups, then there are 30 PG-wing combinations. And each of those 30 different PG-wing combinations can work with 10 different big combinations, so there must be 300 total different lineups.

So, while it's true I have had a lot of higher math (B.S. degrees in both physics and math, followed by M.S. and Ph.D. degrees in Physics), the hard thing for this particular calculation was just figuring out what needed to be done.
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It's interesting to see education system differences. Permutation and combination are thought in 6th (simpler) and 8th (complex) grade math classes in Turkey.
 
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