To solve this problem, we can use the concept of combinations and permutations.
1. When the order of selection is not important, it is a combination problem. We can calculate this using the formula for combinations:
The number of ways to select r items from a set of n items is given by:
nCr = n! / (r!(n-r)!)
In this case, we need to select 2 members from a set of 6, so:
6C2 = 6! / (2!(6-2)!) = 6! / (2!4!) = (6*5) / (2*1) = 15
Therefore, there are 15 ways to select 2 members from the ski patrol unit when the order is not important.
2. When the order of selection is important, it is a permutation problem. We can calculate this using the formula for permutations:
The number of ways to arrange r items from a set of n items is given by:
nPr = n! / (n-r)!
In this case, we need to select 2 members from a set of 6, so:
6P2 = 6! / (6-2)! = 6! / 4! = (6*5*4*3*2*1) / (4*3*2*1) = (6*5) = 30
Therefore, there are 30 different arrangements possible when selecting 2 members from the ski patrol unit, and the order of selection is important.