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?

  • $\begingroup$ If you are picking without replacement (which is the natural interpretation, I think) then neither is correct. $\endgroup$ – 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 $\dfrac{15}{56}$

  • $\begingroup$ are you assuming that the balls are unique? Whats the answer if the balls of a certain color are alike? $\endgroup$ – kartik trivikram Sep 12 '15 at 20:10
  • $\begingroup$ @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. $\endgroup$ – barak manos Sep 12 '15 at 20:29
  • $\begingroup$ Got it! .. Considering this is executed without replacement .... Your answer is same as 3/8*2/7*5/6 + 3/8*5/7*2/6 + 5/8*3/7*2/6 $\endgroup$ – kartik trivikram Sep 13 '15 at 15:30

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