If each ball is considered unique irrespective of colour, the number of ways of selecting 3 from 9 balls is 9*8*7/(3*2*1)=84. This is a combination of balls, so the order in which they are selected is not important.
If the balls are identified only by their colour, we can find out the possible combinations as follows. Remember there are only two blue balls.
| |
Red |
White |
Blue |
| Blue |
BR |
BW |
BB |
| White |
WR |
WW |
|
| Red |
RR |
|
|
The above table covers all combinations of 2 balls. There are 6.
| |
BR |
BW |
BB |
WR |
WW |
RR |
| B |
BBR |
BBW |
X |
BWR |
BWW |
BRR |
| W |
|
|
|
WWR |
WWW |
WRR |
| R |
|
|
|
|
|
RRR |
The above table shows the results of combining the 2-ball combinations with the third ball.
X means nor permitted because there are only 2 blues. So, as long as it's only combinations of colours, not permutations or unique arrangements, there are only 9 ways to select the balls as given. The empty cells in both tables means that we have already included the combination elsewhere.