A box contains 10 balls, which are 6 W and 4 B. Assume you pick one by one, without replacement

Question

What is the probability that only $1$ out of the first $4$ you picked are black?

So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:

$\mathrm{BWWW}$

$\mathrm{WBWW}$

$\mathrm{WWBW}$

$\mathrm{WWWB}$

$4$ ways to orient this.

There are $6$ W balls, from those we must pick $3$.

There are $4$ B balls, from those we must pick $1$.

Thus:

$$\frac{\displaystyle\binom{6}{3}\binom{4}{1}}{\displaystyle\binom{10}{4}}$$

Is this correct?

Answer 1

Your answer is correct and is a good example of use of the hypergeometric distribution.