One a musical instrument with four valves, how many different fingerings are possible?

Question

all work please? Thanks

Answer 1

16

2 x 2 x 2 x 2

The valves can be open (O) or closed (C)

CCCC

CCCO

CCOC

COCC

CCOO

COOC

COCO

COOO

OOOO

OCOO

OCCO

OCCC

OCOC

OOOC

OOCO

OOCC

Answer 2

There are four valves, each with two positions (open and closed).  The number of different fingerings is therefore 2^4, or 16.  If each valve had three possible positions (say, open, half-open, and closed), then the number would be 3^4, or 81.

Note that on many instruments different fingerings will result in the same note.  However, this should not affect the answer since you asked about fingerings, not notes produced.

Answer 3

its 16..........

2^n

where in n=4

then 2x2x2x2

=16

thats it!

Answer 4

4 x 3 x 2 x 1 =24

Answer 5

For each valve, there are two options.  So, you have

2x2x2x2

16.

Answer 6

4! (read four factorial)

4!=4x3x2x1=24

24 possible combinations;