Question

A student club has 11 members. How many ways can the club choose a president, vice president, and treasurer?
A. 330
B. 990
C. 165
D. 1,650

Answer 1

The easiest way to do this is this:

11 members can be president
11 members can be vice president
11 members can be treasurer

11*10*9
990

Answer 2

A student club has 12 members. How many ways can the club choose a President, Vice President, Secretary, and Treasurer?


12,300

11,880

6,940

9,940

Answer 3

Yes, and it would be 12*11*10 because there are three positions. After the position of president is filled, there are only 10 members that can fill vice president and treasurer. After vice president is filled, there are only 9 members who can fill the treasurer position. Make sense?

Answer 4

I don't know what happened it deleted the question but thank you !

Answer 5

So in this case, there's four positions. So it'll be 12*11*10*9 right?

Answer 6

So, the answer would be 11, 880? :)

Answer 7

12 members can be president.
After the president is filled, only 11 members can be vice president, treasurer, and secretary.
After the vice president is filled, only 10 members can be treasurer or secretary.
After the secretary is filled, only 9 members can be treasurer.

You're correct, yes

Answer 8

This is making so much sense now thank you so much! Can you help me with this one:

P(7,3) =

I have no idea what to do

Answer 9

Are there directions for that?

Answer 10

Evaluate?

Answer 11

I think so, but they're so complicated for me.
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P(n,r)

This symbol is read, "P of n comma r."

Note: Sometimes P(n,r) is written nPr.

To describe the problem you just solved, you would say that P(7,3) = 210, because that's the number of permutations of length three that you could form from the set, {A,B,C,D,E,F,G}.

There is a formula to compute P(n,r) directly. You don't need the formula, because you can always answer questions about permutations using the multiplication principle. But permutations come up enough that this formula is useful.
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I know it says the answer but I don't know how to do it on my own.

Answer 12

I'm getting 840 for that, I'm not sure how it gets 210. Sorry.

Answer 13

Nevermind, I do know

Answer 14

I'll explain it

Answer 15

So here's the formula you're going to use: