vertigo05 wrote:A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.
A. 48
B. 288
C. 495
D. 990
E. 11880
Whenever we're choosing subgroups out of a big group, we want to think about either combinations or permutations.
Next, we want to ask ourselves if order matters. Here it clearly doesn't ("if the order of selection doesn't matter"), which means that we have a combinations question.
In general:
nCk = n!/k!(n-k)!
in which:
n = total number of objects available
k = number of objects included in the subgroup
So, applying the forumla to this question:
12C4 = 12!/4!(12-4)! = 12!/4!8! = 12*11*10*9/4*3*2*1
(shortcut applied above: cancel out the bigger factorial on the bottom with part of the factorial in the top; since 12! = 12*11*10*9*8*7*6*5*4*3*2*1, we can rewrite it as 12*11*10*9*8! and then cancel out the 8! on top and bottom of the fraction)
= 12*11*10*9/4*3*2 = 11*10*9/2 = 99*5 = 495... choose (C).
