On a muscial instrument with 4 valves how many different fingerings are possible?

Question

On a muscial instrument with 4 valves how many different fingerings are possible?

Answer 1

Hi - first, remember that a fingering could use 1, 2, 3, or all 4 valves.

There are 4 fingerings that each use 1 valve (1, 2, 3, and 4).

There are 6 fingerings that each use 2 valves (1-2, 1-3, 1-4, 2-3, 2-4, and 3-4).

There are 4 fingerings that each use 3 valves (1-2-3, 1-2-4, 1-3-4, and 2-3-4).

And there is only one fingering that uses all 4 valves.

So the total possible number of fingerings is (4 + 6 + 4 + 1), or 15.

Hope this helps!