[ Rule of product ] [ Combinations and arrangements ]

A rook stands on the leftmost cell of a $1 \times 30$ strip and can move any number of cells to the right in one move.

a) In how many ways can it reach the rightmost cell?

b) In how many ways can it reach the rightmost cell in exactly seven moves?
a) She may or may not visit each of the 28 non-edge fields.

b) We need to choose 6 fields where she will make stops.

## Answer

a) $2^{28}$; b) $\mathrm{C}_{28}^{6}$ ways.

How many ways can seven coins of different denominations be distributed into three pockets?

## Hint

Each of the coins can end up in any of the three pockets.

## Answer

$3^{7}$ ways.