Question 626167: A 40-member club will elect a president and elect a vice president. How many possible ways can a president and vice president be elected from this club/
Suppose the 40 member club instead elects two co-presidents. How many possible ways can co-presidents be elected from this club?
How are these questions alike and how are they different?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
president vice president
a b
a c
b c
b a
c a
c b
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:
co-president co-president
a b
a c
b c
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.
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