Question

The Cleveland Art Institute has eight paintings by a local artist they plan to display. If the paintings are hung in one horizontal line, how many different ways can they be arranged if order is important?

Answer 1

To determine how many different ways the eight paintings can be arranged in a horizontal line, we need to calculate the number of permutations of 8 distinct objects. The number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial).

For this problem, there are 8 paintings, so we will calculate \( 8! \):

\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1
\]

Now, we will calculate the value step by step:

\[
8 \times 7 = 56
\]
\[
56 \times 6 = 336
\]
\[
336 \times 5 = 1680
\]
\[
1680 \times 4 = 6720
\]
\[
6720 \times 3 = 20160
\]
\[
20160 \times 2 = 40320
\]
\[
40320 \times 1 = 40320
\]

Thus, the total number of ways to arrange the 8 paintings is:

\[
\boxed{40320}
\]