Hello!
7P5 is read as "is read "the number of permutations of 7 different things taken 5 at a time".
This means that each arrangement represents a different arrangement of 5 things out of a group of 7 things.
To show this, it would be written as: [tex]nPr = \frac{n!}{(n-r)!}[/tex]. In this case, n is equal to 7 and r is equal to 5.
[tex]7P5 = \frac{7!}{(7-5)!}[/tex] (simplify the parentheses and simplify the factorial)
[tex]7P5 = \frac{7 * 6 * 5 * 4 * 3 * 2 * 1}{2 * 1}[/tex] (simplify the fraction)
[tex]7P5 = 2520[/tex]
Therefore, the answer is the third choice, 2520.