M3tm4n wrote:

I am struggling with this question to solve (Source:its from a math book)

There are 3 black balls and 10 white balls.

if one is to pick 5 balls, What is the probability of picking 2 black and 3 white?

Answer I got:

\(\frac{C^3_2*C^{10}_3}{C^{15}_5}=28%\)

Is there another approach?

Picking simultaneously is same as picking one after another.

So, let's see the probability of picking BBWWW.

(3/13)*(2/12)*(10/11)*(9/10)*(8/9)

But there are many other ways possible e.g. BWWWB, WWBBW etc

Number of all such arrangements = 5!/(2!*3!)

Required answer = (3/13)*(2/12)*(10/11)*(9/10)*(8/9)*5!/(2!*3!) = 40/143

_________________

Karishma

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