Problema Solution
A small acting club has 6 members. Three of the members are to be chosen for a trip to see a Broadway play. How many different 3-member groups are possible?
Answer provided by our tutors
A combination is a way of selecting members from a grouping, such that the order of selection does not matter.
The number of k-combinations from a given set S of n elements is C(n, k) = n!/(k!(n-k)!)
In our case n = 6 and k = 3
C(6, 3) = 6!/(3!(6-3)!)
C(6, 3) = 4*5*6/(2*3)
C(6, 3) = 20
there are 20 different 3-member groups possible.