Number of Permutations with Repetition/Examples/7 Choices from 4

Example of Use of Number of Permutations with Repetition

Residents of a boarding house are offered a choice of $1$ of $4$ main foods for breakfast:

fish or eggs or bacon or sausages.

Over the course of a week, a resident can then order:

$1$ of $4$ dishes on Monday

$1$ of $4$ dishes on Tuesday

$\ldots$

$1$ of $4$ dishes on Sunday

The number of different breakfast arrangements over a week of $7$ days is:

$4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 16 \, 384$

1932: Clement V. Durell: Advanced Algebra: Volume $\text { I }$ ... (previous) ... (next): Chapter $\text I$ Permutations and Combinations: The $r$, $s$ Principle: Example $3$.