2024 DMC Mock 10 Problems/Problem 11
Revision as of 12:09, 22 December 2024 by Pateywatey (talk | contribs) (Created page with "First we use complementary counting to count the total number of possibilities. There are <math>4! = 24</math> ways to arrange the officers without restrictions, and <math>2 \...")
First we use complementary counting to count the total number of possibilities.
There are 
ways to arrange the officers without restrictions, and 
ways if the
treasurer and president sit next to each other, so the officers can sit in a total of $24 − 12 = 12$ (Error compiling LaTeX. Unknown error_msg)
ways. Similarly, there are 
ways for both the treasurer and vice president to sit next to the
president. Therefore, the answer is 
.
