An octave contains twelve distinct notes (on a piano, five black keys and seven white keys). how many different eight-note melodies within a single octave can be written if the black keys and white keys need to alternate?

Ok, so you have 8 white notes and 5 black.

You want to write an 8 note melody, with te only restriction that you need to alternate the colors.

so if we start with the white keys you have

8 possibilities, then 5, then 8, then five, and so on.

so you have

and also you can start with a black key, that will give you the same amount of combinations.

so total number is 2* = 512000

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

i hope this is what you were looking for.

see attached graph