Question

medal!


How many combinations of a president, vice-president, secretary, and treasurer can be chosen from a group of 12 students?

11,880
95,040
665,280
3,991,680

Answer 1

This is permutations correct?

Answer 2

yesss

Answer 3

@Luigi0210

Answer 4

Do you know the formula for permutations?

Answer 5

yes nPr+ n!/ (n-2)

Answer 6

Just plug in values :)

Answer 7

but the answer...we dont have this option

Answer 8

!

Answer 9

Wait, nvm it's a combination!

Answer 10

please just help me

Answer 11

@Luigi0210

Answer 12

Think of the different positions as 4 seats. For the first seat we can choose from 12 students, for the second we have 11 students left to choose from, continuing we get:
\[ 12\times11\times10\times9=11880 \]

Answer 13

This can also be written as
\[ \frac{12!}{(12-4)!} \]
Which hints at the general formula for permutations
\[ \frac{n!}{(n-k)!} \]
Where \(n\) is the number of choices have for each "seat" and \(k\) is the number of "seats".