# clubs

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```					Alice   Bob   Celia Don    are members of a club.
Bob         In how many ways can they select
Alice     Celia      a president and vice president ?
Don            4 x 3 = 12
Alice
Bob        Celia
Don

Alice
Celia    Bob
Don
Alice
Don      Bob
Celia
Alice   Bob   Celia Don    are members of a club.
Bob           In how many ways can they select
Alice     Celia        a 2 person committee?
Don
1.)
Alice
Bob        Celia                           2.)
Don

Alice                             3.)
Celia    Bob
Don                               4.)

Alice                             5.)
Don      Bob
Celia                             6.)
Alice      Bob   Celia are running for pres., vice pres., and secretary
Bob        Celia
Alice                                               There are 6
Celia      Bob                        different ways
Alice      Celia                      of arranging
Bob                                                 3 people in
order.
Celia      Alice
Alice      Bob
Celia

Bob        Alice

The number of possible outcomes = 3 x 2 x 1 = 6
Alice   Bob    Celia Don      Edna     are members of a club.

In how many ways can they select a pres., vice pres., and secretary?

There are 5 ways     For each of the 5 ways          For each of the 20
to select a pres.    to select a pres., there are    ways to select pres.
4 ways to select a vice pres.   and vice pres.,
there are 3 ways to
select a secretary.
5 x 4 x 3 = 60
In how many ways can they select a
3 person committee?

Alice   Bob Celia Don   Edna

There are 60 branches on this tree -
60 ways to select 3 people in order

But each 3 person committee
is repeated 6 times on this
list of 60.
In how many ways can they select a
3 person committee?

Alice   Bob Celia Don   Edna

This one committee appears 6 times
In how many ways can they select a
3 person committee?

Alice   Bob Celia Don   Edna

And this committee appears 6 times
Alice    Bob     Celia Don       Edna   are members of a club.

The number of ways of selecting
a pres., vice pres., and secretary       =      5x4x3

the number of repetitions of each
3 person committee                       =       3x2x1

The number of 3 person committees = 5 x 4 x 3 = 10
3x2x1

```
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