Answer:
35,829,630 melodies
Step-by-step explanation:
There are 12 half-steps in an octave and therefore arrangements of 7 notes if there were no stipulations.
Using complimentary counting, subtract the inadmissible arrangements from to get the number of admissible arrangements.
can be any note, giving us 12 options. Whatever note we choose, must match it, yielding . For the remaining two white key notes, and , we have 11 options for each (they can be anything but the note we chose for the black keys).
There are three possible arrangements of white key groups and black key groups that are inadmissible:
White key notes can be different, so a distinct arrangement of them will be considered a distinct melody. With 11 notes to choose from per white key, the number of ways to inadmissibly arrange the white keys is .
Therefore, the number of admissible arrangements is:
I think it’s pretty interpretative, the reason I didn’t divide 483/2 like you would normally with a triangle, is because there are 2 triangles in a trapezoid. Also you can split the two triangles off the trapezoid because in a trapezoid the train for will awkward be right.
No. 10/9 would be bigger than 1.
If (3)
x+y
=81 and (81)
x−y
=3, then the values of x and y are 17/8 and 15/8
Step-by-step explanation: