An urn contains $12$ balls, of which $7$ are black and $5$ are white. How many ways can we take $6$ balls out of the urn, $2$ of which are white? Uma urna contém $12$ bolas, das quais $7$ são pretas e $5$, brancas. De quantos modos podemos tirar $6$ bolas da urna, das quais duas sejam brancas? The original text is in Portuguese; an English version is: "An urn contains $12$ balls, of which $7$ are black and $5$ are white. How many ways can we take $6$ balls out of the urn, $2$ of which are white?"

If the balls are indistinguishable, then there are $1$ ways, because you could take $2$ white balls and $4$ black balls.

If the balls are distinguishable, then you would have $\binom{5}{2}$ ways to choose $2$ white balls and $\binom{7}{4}$ ways to choose the $4$ black balls, leading to $350$ ways total.