Question

A hat contains three gold coins, two silver coins and one copper coin. We will select
coins without replacement until the first silver coin is selected. The outcome of interest
is the sequence of coins that are selected during this process. How many outcomes are
in the appropriate sample space for this experiment?
The answer is 14.
I really not good at counting sample space. can anyone give me some tips?

Answer 1

I can start the sample space:
{ S, GS, CS , GGS, GCS, CGS, CCS, GGGS, ... }

Answer 2

oops one copper coin

Answer 3

{ S, GS, CS , GGS, GCS, CGS, GGGS, GGCS, GCGS, CGGS,
GGGCS , GGCGS, GCGGS, CGGGS }

Answer 4

@perl does it has a mathematic way or formula to do the sample space? Or I need to list all the outcome all the times??