# Probability of picking balls from jar

Suppose a jar contains 8 balls among which 5 are red and 3 are blue. If i pick, 3 balls from this jar, what is the probability that "exactly" two of them are blue ball?

• If you are picking without replacement (which is the natural interpretation, I think) then neither is correct. – André Nicolas Sep 12 '15 at 20:00

The total number of ways to choose $3$ out of $8$ balls is $\binom83=56$
The number of ways to choose $2$ out of $3$ blue balls and $1$ out of $5$ red balls is $\binom32\cdot\binom51=15$
Hence the probability is $\dfrac{15}{56}$
• @karthikts: It doesn't make any difference. There are $56$ (not necessarily different) ways to choose $3$ out of $8$, and $15$ of them contain exactly two blue. – barak manos Sep 12 '15 at 20:29