Question

Statistics help anyone?

Four members from a 17-person committee are to be selected randomly to serve a schairperson, vice-chairperson, secretary, and treasurer. The first person selected is thechairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible?

Answer 1

So,

we have 4 positions and 17 people

once we find someone from the 17 people to take the first position, we are left with 16 people to take the second position.

And then we have 15 people for the third position, and then 14 for the last position.

This is a permutations:

17P4

Answer 2

So, how would I know if it's permutations or combinations?

Answer 3

permutation -- order matters
combination -- order does not matter

Answer 4

How would I know this is permutation? It doesn't nessacarily let you know. Unless there's hints I do not know.

Answer 5

\(\bf\Large ^nP_r = \frac{n!}{(n-r)!}\)

\(\bf\Large ^nC_r = \frac{n!}{r!(n-r)!}\)

Answer 6

"The first person selected is thechairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer."

These lines show us that order is important. You have to first choose the chair person before you can choose the vice-chairperson and before you can choose the secretary and then after you choose all those people, you can finally choose the treasurer

Answer 7

Gotcha. Thanks:) i know how to solve it it's just that I didn't really know which one of those it was.

Answer 8

for example, if they said:

selecting 4 people out of 17 people to have a leadership position

this is an example of a combination

Answer 9

It was my pleasure! :)