Answer:
There are 9,294,695,280 different ways to choose the officiers.
Step-by-step explanation:
The first thing we need to count is all the "selections", then we need to find the number of options for each one of these selections.
The selections are:
president
vice-president
secretary
treasurer
So we have 4 selections, now let's find the number of options for each one.
President: Here we have 312 options (the number of students).
Vice-president: Here we have 311 options (because one of the students was selected to be president)
Secretary: Here we have 310 options (because 2 students where already selected for the two previous positions)
Treasurer: Here we have 309 options.
The total number of different ways to select the officers is equal to the product between the numbers of options, this is:
C = 312*311*310*309 = 9,294,695,280
There are 9,294,695,280 different ways to choose the officiers.
