Hi guys, having a little trouble distinguishing the two.
Comb = unordered where order doesen't matter.
perm = order matters.Combination is 'selection/picking people out of a group'
Permutation is 'arrangement'
Try using the terms selection and arrangement.
But, look at this questions:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
To me, the second part of the question looks like a perm. Since there are 2 seats and therefore 2 candidates (hence they are distinguishable) wouldn't it be 10!/8!=90?We are given that the 2 seats are identical i.e. you just need to select 2 people. You don't have two different positions (e.g. a professor and an assistant professor). The positions are identical so there is no arrangement here. If the positions were not identical, then we would select two people (e.g. Mr A and Mr. B) and then arrange the two people in the two positions i.e. Mr A is professor and Mr. B is assistant professor OR Mr A is assistant professor and Mr B is professor. We would have 2 different arrangements in that case. That would have been a permutation. Right now, since the two positions are exactly the same, you only have to select two people. This is just a combination.
I know I am wrong. Can someone clarify how I can make a better decision distinguishing the two.
Look at another one:
The principal of a high school needs to schedule observations of 6 teachers. she plans to visit one teacher each day for a work week (M-F) so will only have time to see 5 of the teachers. How many different observation schedules can she create?
To me there is no order here as the principal can meet any of the 5 teachers any day! The order in which she meets those "5" selected teachers does not matter. Hence, shouldnt this be a combination problem?
Am I missing some key rule here? or am I just losing it!
Focus on the question - always. It asks you the number of different schedules she can make. Are the following 2 schedules different or not?
Mon - Mr A
Tue - Mr B
Wed - Mr C
Thu - Mr D
Fri - Mr E
Mon - Mr E
Tue - Mr A
Wed - Mr C
Thu - Mr D
Fri - Mr B
I hope you agree that the two schedules are different. So here, you choose 5 people out of 6 and then arrange the 5 on 5 different days. Let's say, I chose Mr A, B, C, D and E. Now I need to arrange them on Mon, Tue, Wed, Thu and Fri. Hence we need to choose and arrange here. This is a permutation.