Review question

# In how many ways can we arrange $4$ white, $3$ black, and $2$ red marbles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9341

## Question

1. 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.]

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