okay.... i just need a quick explanation on what a number like this would translate to:
1.3e+171
that's what i got when i did 88^88
and what i am looking for is all possible combinations on an 88-key piano
is this correct?
Printable View
okay.... i just need a quick explanation on what a number like this would translate to:
1.3e+171
that's what i got when i did 88^88
and what i am looking for is all possible combinations on an 88-key piano
is this correct?
When you say 88 key combinations do you mean of pressing 2 keys at a time? Or up to 88 keys at a time?
lets say both...
1 key at a time, and all the possible sequences
and also 88 keys at a time..
Are you using elemination? After it's been struck once it can't eb struck again? Because if not then your answer is literally infanity.
1 Key at a time should be 89! I think, if I'm thinking right.
that would be 13 with 170 zeros after it
but i don't think you 88^88 calculation is right;
i think its 88! but im not sure
okay... i am limited to the 88 keys for the total sequence... and the key can be used more than once as long as the squence is different...
lets say i started bottom scale, then went to the top... there's one iteration... now i restart, but i stike one key ahead, then finish with the key 1...
make sense?
now i've confused myself. ;)
Assuming you don't have to go in order with the keys...88^88 because (if this makes sense)
The first time you hit a key you have a choice of 88 keys. The next time you still have a choice of 88 keys (assuming you can press the same key again). You do this 88 times.
Answer is roughly:
1.3e+171 - like you origanally said, also said as:
1.3x10^171
or 13 with 170 0s after it.
1.3e+171
Is the same as:
13000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000
thanks for the confirmation kermi
All possible keypresses on an 88 key piano? Wouldn't that be n*n-1, or nn-n. So, 88*88-88 = 7656 possible combinations
Permutations versus Combinations
Permutations (order is important)
P(n,r) = n!/(n-r)!
Combinations (order in NOT important)
C(n,r) = n!/(r! * n!)
Haha funny this is just the math class im in, math 3322 Discrete Modeling, study of combinatorics and graph theory
anyways what you have is you have 88 keys on the piano. You want the number of ways you can pick any 2 keys from the total 88.
So you have 88 choose 2 where n = 88 and k = 2, and x is the soulotion you have:
x = n!/(k!(n-k)!) = 88!/(2!(88-2)!) = 88!/(2!(86)!)
= (88*87*86!)/(2!(86!)) = (88*87)/2! = 7656/2 = 3828 2 key combinations
[EDIT]
if you have a TI 81/82/83 and above you can check this by doing this:
88[Math]->PRB->3(nCr)2 = 3828
where [Math] is the math key -> implies press over to the PRB menu->3 is the function to select, well at least on my Ti83, but look for nCr
That's the same as 1 / (r!)... are you sure you're right ;)Quote:
Originally posted by Bajanine
C(n,r) = n!/(r! * n!)
Wow, did I ever butcher that. I believe it is:
C(n,r) = n!/(r! (n-r)!)
Just as xds4lx posted!