To find out how many ways the local painter can display 4 out of 8 of his favorite paintings, you can use the concept of combinations.
Here's how you can calculate it step-by-step:
1. Determine the total number of ways to choose 4 paintings out of 8. This is denoted as "8 choose 4" and can be calculated using the formula:
\( \binom{8}{4} = \frac{8!}{4!(8-4)!} \)
2. Simplify the calculation:
\( \binom{8}{4} = \frac{8!}{4!4!} = \frac{8*7*6*5}{4*3*2*1} = 70 \)
Therefore, the local painter can display his 4 favorite paintings in 70 different ways. Each of these ways represents a unique combination of 4 paintings chosen from the total of 8.
