# Probability of picking three M&Ms of the same color from a bag?

I just pulled three M&Ms from a bag that were all orange, and I wanted to determine what the probability of this happening is. (This is unordered sampling without replacement.)

Assuming that:

• There are 11 orange M&Ms in a bag
• There are 55 total M&Ms in a bag

Then I calculate that the probability of pulling three oranges from the bag are:

$\dfrac{\text{all the ways to pull three oranges from the bag}}{\text{all the ways to pull three of any color from the bag}} = \dfrac{{11}\choose{3}} {{55}\choose{3}} = 0.0062$

Is this correct, or am I mistaken?

• The probability is closer to $0.0063$, but the procedure is correct. There are other ways, such as $\frac{11}{55}\cdot\frac{10}{54}\cdot \frac{9}{53}$. – André Nicolas Jan 2 '14 at 4:35
• Perhaps you wish to use the word probability instead of odds...? – Benjamin Dickman Jan 2 '14 at 7:28