I've Got Rhythm

Probability Level 3

In the common time meter, one bar of music consists of note values equivalent to 44 quarter notes. Using the note value system, 11 whole note is equivalent to 22 half notes, 11 half note is equivalent to 22 quarter notes, 11 quarter note is equivalent to 22 eighth notes, and 11 eighth note is equivalent to 22 sixteenth notes. (For our British friends, a whole note is a semibreve, a half note is a minim, a quarter note is a crotchet, an eighth note is a quaver, and a sixteenth note is a semiquaver.)

An example of a rhythm in one bar of common time meter with 11 quarter note, 22 sixteenth notes, 11 eighth note, and 11 half note is shown below.

Using only whole notes, half notes, quarter notes, eighth notes, and sixteenth notes (with no rests or dotted modifiers), how many unique rhythms can be made in one bar of common time meter?

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