PLEASE HELP There are 312 students in the senior class. Four of the students will be chosen to be the
President, Vice-President, Secretary, and Treasurer of the class. How many different ways
can this happen?
There are ___ different ways to choose the officers.

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.

there are no multiple choices