The seven pictures can be hanged in 5040 ways in a straight line.
Explanation:
It is given that, there are seven pictures that are to be hanged in a straight line in many ways.
The seven pictures can be arranged in several ways which can be found using the factorial.
Since there are 7 different pictures, the number of ways it can be arranged is 7 factorial ⇒ 7!
if we are filling the 7 pictures at a time, we have seven options to fill the first position.
And then, there are 6 options to fill the second position and followed by the third position which as 5 options to filled and it continues till the seventh position which will have only 1 option to be filled.
Therefore, it is calculated as :
⇒ 7! = 7×6×5×4×3×2×1
⇒ 5040 ways.
The seven pictures are hanged in 5040 ways.