a permutation is like you want to select x people from a group of y people
the formula is x*(x-1)*(x-2)*...../y!
(e.g. 4 people from 12 people)
12*11*10*9/4! = 11880/24=495 (ways)
What you have described in words is a combination
For example, 3 people are chosen from 10. How many COMBINATIONS are possible 10C3=120 would be the answer?
For permutations, order matters.
For example. 10 people run in a race, how many PERMUTATIONS are possible for 1st, 2nd and 3rd places.
This is the same as: choose 3 from 10 when order matters. 10P3=720 ways.