Answer:
24 different ways.
Explanation:
To determine the number of ways the photographer can arrange the four pictures for a gallery showing, we can use the concept of permutations.
In this case, since the order of the pictures matters (each picture will be displayed in a different order), we can use the formula for permutations:
n! / (n - r)!
Where n is the total number of pictures (4 in this case) and r is the number of pictures to be selected (also 4 in this case).
Plugging in the values, we have:
4! / (4 - 4)!
= 4! / 0!
= 4! / 1
= 4 x 3 x 2 x 1 / 1
= 24
So, the photographer can arrange the four pictures in 24 different ways for the gallery showing.
The formula for permutations can be used in similar situations where the order matters and repetition is not allowed.