A ski patrol unit has six members available for duty, and two of them are to be sent to rescue an injured skier. In how many ways can two of these six members be selected?

Now suppose the order of selection is important. How many arrangements are possible in this case?

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.