Just wondered if someone could help me with this...

There are 52 white keys on a piano. The lowest key is A. The keys are designated A,B,C,D,E,F, and G in succession, and then the sequence of lettesr repeats, ending with a C for the highest key.

a) If five notes are played simultaneously, in how many ways could all the notes be:

i) As?

ii) Gs?

iii) the same letter

iv) different letters

b) If the five keys are played in order, hwo would your answers in a) change?

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Okay, so, I've figured out i, ii, and iii for part a, I think..

i) $\displaystyle {8 \choose 5}$ (because A is one of the keys that are repeated at the end)

ii) $\displaystyle {7 \choose 5}$

iii) $\displaystyle {3}{8 \choose 5} + {4}{7 \choose 5}$

And for part b, obviously you just do the math as permutations rather than combinations.

But for Part a, iv), I'm confused about how I should answer. If all they care about is 7 different keys, then your answer would obviously be $\displaystyle {7 \choose 5}$. But, this wouldn't be taking into considering that you could be playing an A in one octave, and a B in another octave. A lower B does not sound the same as a higher B. Is this what the question is indeed looking for? and if so, how would I solve that?

Thanks!