Math Is Fun Forum

NESIC

Member

Registered: 2010-09-25

Posts: 16

Permutation or Combination i am Confused

Find the number of ways in which 06 teachers can be assigned to 04 sections of an
introductory psychology course?
a. If no teacher is assigned to more than one section.
b. If a teacher can be assigned more than one section.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,631

Re: Permutation or Combination i am Confused

Hi NESIC,

Let's call the teachers A, B, C, D, E, and F.  Is the arrangement ABCD different from BDCA, for example?

I'd say YES because, from a teacher's point of view being in the same group of four, but teaching a different section is different.  So this is more like a permutation than a combination.

If you were picking different sweets from a bag, picking ABCD would be the same as picking BDCA if you can eat them in any order, so it would be a combination problem. 

(i)   Choose the first teacher.  6 choices.
      Choose the next.             5 choices.
      Choose the next.             4 choices.
      Choose the last.              3 choices.

So there are 6 x 5 x 4 x 3 ways of doing this.

(ii)    Choose the first.             6 choices.
        Choose the next.     Still  6 choices.
        Choose the next      Still  6 choices.
        Choose the last.      Still  6 choices.

So there are 6 x 6 x 6 x 6 ways this time.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob