# probability to get the black ball when taking 4 elements from a set of balls

I have a question about probability that seems to be more difficult than I thought:

We assume we have a set of $x$ balls: all of them are white except one that is black ($x-1$ white ball and $1$ white ball)

We take $4$ balls from the set at once. Would please help me calculate the probability that this set contains the black ball?

Thanks!

HINT: Calculate the probability that it does not contain the black ball, and subtract from $1$. How many $4$-ball sets are there that do not contain the black ball? How many are there altogether?
• So,you propose: $P(black ball)=1-C_{4}^{x-1}$, right? – ra7ma Nov 15 '13 at 15:25
• @ra7ma: No, because $\binom{x-1}4$ can’t be a probability. Try $$1-\frac{\binom{x-1}4}{\binom{x}4}\;.$$ – Brian M. Scott Nov 15 '13 at 20:18