Question

A club has 20 members.

a) How many ways are there to choose four members of the club to serve on an executive committee?

[Num] ways

b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

[Num] ways

Answer 1

For problems like this, you have to decide if you're working with "combinations" or "permutations." Hopefully those sound familiar?

Answer 2

this is a permutation/combination question
are you familiar with the concept?

Answer 3

part 1 would be 20C4, which is 20!/((20-4)!*4!
do the math.

Answer 4

A combination is what you'd use if you're choosing a group of members, but in no particular order.

So if you're picking a group of people to be on your team for tag.
Permutations are when you're choosing for a group and the order DOES matter.

So for example: choosing people to be the different positions on a baseball team (pitcher, catcher, etc.)
So for part a)...

Answer 5

@lucian_denvers41325 Please refrain from giving direct solutions, it hinders the learning process.

Answer 6

yea i forgot how to work them I came up 116280 for part one and now just trying to remember part two

Answer 7

one is not right because i forgot a step

Answer 8

So notice that each person has a specific job, right?
so that tells us it's which type? combination or permutation? @vortish

Answer 9

i came out with 4845 for part one

Answer 10

ok, for part 2 out of the 4 people youve chosen for the executive committee, you get t0 pick one for each position. for the first position, you have 4 choices of people. you chose one of the 4 people. for the second post you have 3 choices, cuz you already reserved one person for the 1st post, and so on. i guess that should explain what you should do.

Answer 11

its a permutation

Answer 12

Right, and I got the same for part a) 4845

Answer 13

So back to the permutation in part b).

What you can do is figure out how many options you have for the first position, which is the president. How many different people could be chosen to be president?

Answer 14

you have four for the 1st postison three for the second two for the third and one for the last

Answer 15

Well, there are 20 people total, though, right?
So any of those 20 people could be chosen to be the president.

So we have 20 options that for position.

Answer 16

B) _20_ __ __ ___

Answer 17

Now after you choose the president...
how many people are left to choose the vice pres from?

Answer 18

Remember - no person can hold more than one office.

Answer 19

19 for the second 18 for the third and 17 for the last

Answer 20

So we can't use whichever person was just chosen to be president.

Answer 21

And right!

Answer 22

Then you just multiply those.
So like this:

20 * 19 * 18 * 17 = ?

Answer 23

116280

Answer 24

Yay! Good job! =]

Answer 25

k thanks

Answer 26

yw

Answer 27

can you help me with another one