Question 626167
n = 40
want to elect a president and vice president.
formula is P(40,2)
P is for permutation with n = 40 and x = 2.
the number of possible permutation is equal to 40! / (38!) which becomes:
40 * 39 = 1560


n = 40
want to elect 2 co-presidents.
formuls is C(40,2)
C is for combination with n = 40 and x = 2.
the number of possible combinations is equal to 40! / (38! * 2!) which becomes:
40 * 39 / 2 = 1560 / 2 = 780


the difference is in the first case order was important and in the second case order was not.


this is easier to see if n = 3.
you want to elect a president and vice president.
the formuls now becomes P(3,2) which becomes 3! / 1! which becomes 3*2 = 6 possible ways.
those ways are:
<pre>
president     vice president
     a             b
     a             c
     b             c
     b             a
     c             a
     c             b
</pre>
order was important because candidate A could be president or vice president.
now you want to elect 2 co-presidents.
the formula now becomes C(3,2) which becomes 3! / (1! * 2!) becomes 3*2/2 = 3
those ways are:
<pre>
co-president     co-president
     a               b
     a               c
     b               c
</pre>
order was not important here since there is no difference between a co-president and a co-president
candidate A can be one of the candidates for co-president while candidate B can be one of the candidates for co-president - which co-president position each takes doesn't matter.