SOLUTION: A total of 72 different two-item outfit permutations can be created from a pile of clothes containing A. 2 garments B. 8 garments C. 9 garments D. 10 garments

We can choose the first item in n ways.

For each of those n ways to choose the first item,
we can choose the second item any of the n-1 remaining ways.

That's n(n-1) ways.

For that number to be 72 the solution would be the solution
to the equation

        n(n-1) = 72

        n² - n = 72 

   n² - n - 72 = 0

(n - 9)(n + 8) = 0

n-9=0;  n+8=0
  n=9;    n=-8

Ignore the negative answer.

Solution:  9 garments.

Edwin