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? A.10,880 B.20,160 C.1 D.40,320

Answer 1

40320 bro gotchu bruh

Answer 2

40320 ways

Explanation:

Given

Paintings = 8

Required

Determine the number of arrangements

From the question, we understand that the order of arrangement matters;

This implies permutation and is calculated as thus;

`^nP_r = (n!)/((n-r)!)`

In this case,

`n = 8`

`r = 8`, because all paintings are hung;

Substitute 8 for n and r, respectively

`^8P_8 = (8!)/((8-8)!)`

Evaluate the denominator

`^8P_8 = (8!)/(0!)`

`^8P_8 = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(1)`

`^8P_8 = 40320`

Hence, the number of arrangement is 40320 ways