Question

A club has 18 members. In how many ways can 4 officers consisting of a president, vice-president, secretary, and treasury be chosen? Fill in the blank with your answer which should be a positive integer

Answer 1

this is a permutation problem

Answer 2

as was the car one I guess.

Answer 3

how should i set it up?

Answer 4

P (n,r)

Answer 5

is this correct?

Answer 6

Right.

Answer 7

How big is the pool?

Answer 8

18

Answer 9

so could you show me how to set it up? i am still a little confused as tohow to do that

Answer 10

would it be 18!/(18-4)!

Answer 11

so the answer would be 73440?

Answer 12

that number seems kinda big

Answer 13

It is big, and it is correct ;)

Answer 14

positive???

Answer 15

i have one more for you!!!!

Answer 16

you are seriously saving my life right now

Answer 17

You are doing most of the work. I'm just explaining what the question means.

Answer 18

There are 5 different French books and 5 different Spanish books. How many ways are there to arrange them on a shelf if

(a) Books of the same language must be grouped together, French on the left, Spanish on the right?
(b) French and Spanish books must alternate in the grouping, beginning with a French book?

Answer 19

i have noooooooooo clue how to do this one

Answer 20

Ok, which one do you want to do first?

Answer 21

a

Answer 22

Ok, so it's a permutation problem

Answer 23

okay

Answer 24

so do i just set it up normally?

Answer 25

Are you familiar with the product rule for combinatorics?

Answer 26

noooo!

Answer 27

Ok, it's very simple.

Answer 28

If we have to do two different tasks to complete a job. And task 1 has n different ways it can be done. And task 2 has m different ways it can be done. The total different possible ways to complete the job is n*m.

Answer 29

so is it just 5*5?

Answer 30

no!

Answer 31

here we have 2 different tasks to do. First we must arrange the french books, then we must arrange the spanish books.

Answer 32

How many different ways can we permute the french books?

Answer 33

5

Answer 34

no!

Answer 35

how many?

Answer 36

p(5,5)

Answer 37

120

Answer 38

Ok, now we must arrange the spanish books. How many different ways can we do that?

Answer 39

120

Answer 40

So the total number of different ways we can do the whole job is?

Answer 41

240?

Answer 42

no

Answer 43

n*m

Answer 44

14400

Answer 45

correct

Answer 46

and now b?

Answer 47

ok, so tell me what you think about b.

Answer 48

honestly i think it might be the same?

Answer 49

you are exactly right.

Answer 50

you are the best

Answer 51

because we still have to choose how to arrange the french and spanish books. then we just interleave them.

Answer 52

choose how to arrange them separately. I mean.