Answer:
a) This is a permutation, there are 210 ways to do it
b) This is a permutation with 6 possibilities
c) This is a combination with a total of 1081575 possibilities
Step-by-step explanation:
a) Here the order does matter bacause it is not the same that they go to France in the weak trip than they go there for 2 days, as a result, this scenario is a permutation.
You need to pick 3 countries from a total of 7, but the order matters, so the total amount of ways to do this is
b) Here each permutation of 123 will give you a possible (and a different one from the others) lock-combination, so this is again a permutation.
The total amount of ways we have to do the selectio of the lock-combination is the total amount of permutations of a set of 3 elements, in other words, it is 3! = 6.
c) If you only cares about who advances to the finals, then the order doesnt matter here, you just want 8 people out of the 25 available. This is therefore a combination, and the total amount of possible cases are
.