In how many ways can we arrange $4$ white, $3$ black, and $2$ red marbles?

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Show that there are \({}^{10}C_4\) ways of arranging six similar white and four similar black marbles in line.

[Editorial note: \({}^{10}C_4\) is an alternative notation for \(\tbinom{10}{4}\).]

Find the number of ways of arranging four white, three black, and two red marbles in line, assuming that marbles of the same colour are indistinguishable. [A numerical answer is required.]

A bag contains six white and four black marbles. Find the chance that, if two marbles are drawn together, they are both black.