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.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

a

step-by-step explanation:

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