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

40320 ways

Step-by-step 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;

In this case,

, because all paintings are hung;

Substitute 8 for n and r, respectively

Evaluate the denominator

Hence, the number of arrangement is 40320 ways

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.