Chapter 4.1, Problem 46E

To determine

To calculate: The number of ways in which display can be arranged.

Answer to Problem 46E

There can be 1 row of 50 quarters, or 2 rows of 25 quarters in each row, or 25 rows of 2 quarters in each row, or 5 rows of 10 quarters in each row, or 10 rows of 5 quarters in each row.

Explanation of Solution

Given information:

There is one state quarter for each of the 50 states.

The rectangular display same number of quarters in each row

Given that there is one state quarter for each of the 50 states.

Now, write 50 as a product of two of its factors,

  $\begin{array}{c}50=1\times 50\\ 50=2\times 25\\ 50=5\times 10\end{array}$

This implies that there can be 1 row of 50 quarters, or 2 rows of 25 quarters in each row, or 25 rows of 2 quarters in each row, or 5 rows of 10 quarters in each row, or 10 rows of 5 quarters in each row.