[ Arrangements and Partitions ]  [ Combinations and Permutations ]

A train with $m$ passengers is to make $n$ stops.

a) In how many ways can the passengers exit the train at these stops?

b) Solve the same problem if only the number of passengers exiting at each stop is considered.

#
a) Replacing passengers with coins and stops with pockets, we get a problem analogous to problem 60348.

b) This is a rephrasing of problem $\underline{30719}$ b).

## Answer

a) $n^{m} ;$ b) $\mathrm{C}_{n+m-1}^{m}$ ways.

## [ Rule of Product ]

In how many ways can seven white and two black balls be placed in nine pockets? Some pockets may remain empty, and the pockets are considered distinct.

## Hint

First, you need to distribute the white balls (see problem 30317 b), and then the black ones.

## Answer

$C_{15}^{8} C_{10}^{8}=C_{15}^{7} C_{10}^{2}$ ways.