Gr.12 data management

There are 52 white keys on a piano. The lowest key is A. The Keys are designated A. B, C, D, E, F, G in succession, and then the sequence of letters repeats, ending with a C for the highest key.
A) if five notes are played together simultaneously, in how many ways could the notes al be 1) A's. 2) G's. 3) all the same letter. 4) different letters
B) if five keys are played in order, how would your answers in part a)'change?

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  1. There are 7 octaves, plus an extra A,B,C

    A)
    Since there are 8 A keys, there are 8C5=56 ways to pick them.
    For the G keys, there are only 7C5 = 21 choices.
    For any key, consider it like this. Pick a key from the 1st octave. Now there are fewer octaves to pick the other 4 keys. 3 keys (ABC) will have 7 other octaves, and 4(DEFG) will have 6 other octaves. So, you can pick them in

    3*7C4 + 4*6C4 = 165

    For different letters, I expect you can figure that out.

    B
    If these were all permutations, you'd use 7P5 instead of 7C5, and so on.

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