Question 863759: There are nine balls in a basket. Three of these balls are blue, three are red, and three are green. A boy randomly picks three balls from the basket.
How many possible combinations of balls are there?
(I did this question and got the right answer just by brute force counting, but I want to know if there is a way to do this question using proper math. The possible combinations are (B- Blue, R- Red, G- Green):
B-B-B
B-B-R
B-R-R
R-R-R
R-R-G
R-G-G
G-G-G
G-G-B
G-B-B
B-R-G
For a total of ten possible combinations.)
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! For each choice you can pick 1 of 3 balls.
You have 3 choices to make so,
Easiest way to count is to make a chart with 3 columns.
In the 3rd column, place B,R,G alternately for 27 entries.
In the 2nd column, place B for 3 rows, R for 3 rows, G for 3 rows, then repeat.
In the 1st column, place B for 9 rows, R for 9 rows, G for 9 rows.
That will get you all the values.
BBB
BBR
BBG
BRB
BRR
BRG
BGB
BGR
BGG
RBB
RBR
RBG
RRB
RRR
RRG
RGB
RGR
RGG
GBB
GBR
GBG
GRB
GRR
GRG
GGB
GGR
GGG
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