Permutation Questions

[pkolla90]

Hey guys, I'm new to this forum. There are some homework questions posted on my class webpage that has to be done for the next class. Please answer these questions. I'll appreciate it a lot.

Ten different professors stand in a line at the bookstore. Five are mathematicians, three are physicists and two are engineers how many different lines can be formed if
(a) The line begins and ends with an engineer?
(b) All the mathematicians appear consecutively(all next to each other)?
(c) All of the mathematicians or all of the physicists appear consecutively?
(d) no two Physicists appear next to each other?
(e) there are exactly 2 professors between the pairs of Physicists?


2. Repeat Question 1 (all parts), but with only 8 of the 10 professors
getting in line. In part (b) assume all ve mathematicians are in the
line. In part (c) assume either all ve mathematicians or all three
physicists are in the line. In (d) and (e) do not assume that all the
physicists made it into the line.

3. Twenty hockey players show up for try-outs.
(a) In how many ways can a team of 6 be chosen from those trying
out?
(b) In how many ways can three teams of 6 be chosen from those
trying out where one team is called the Leafs the second team is
called the Habs, and the third team is called the Bruins?
(c) In how many ways can this be done if the three teams are not
given names?

 

[pka]

Hey guys, I'm new to this forum. There are some homework questions posted on my class webpage that has to be done for the next class. Please answer these questions. I'll appreciate it a lot.

Ten different professors stand in a line at the bookstore. Five are mathematicians, three are physicists and two are engineers how many different lines can be formed if
(a) The line begins and ends with an engineer?
(b) All the mathematicians appear consecutively(all next to each other)?
(c) All of the mathematicians or all of the physicists appear consecutively?
(d) no two Physicists appear next to each other?
(e) there are exactly 2 professors between the pairs of Physicists?

First, this is not a homework service. We provide help to those who show some effort of their own.
So post what you have done.

Here is the "back-of-the-book" answer to (a): \(\displaystyle 2(8!)\).

No you respond telling why that is correct. And with your attempt on the others.

 

[pkolla90]

I'm sorry to give the wrong impression. This is my freshman year and really don't understand permutations. I'm not planning on taking any math courses. Please help me out. I tried the others but don't know how to do em'. If you can tell me the process maybe I can follow. Thanks.

 

[JeffM]

I'm sorry to give the wrong impression. This is my freshman year and really don't understand permutations. I'm not planning on taking any math courses. Please help me out. I tried the others but don't know how to do em'. If you can tell me the process maybe I can follow. Thanks.

Permutations are simply a way to count correctly. We don't give answers; we give help. We won't be there for your test so giving you answers without giving you understanding is a disservice that we are unwilling to render.

Also please read Read Before Posting. You will see there, among other things, that we REALLY prefer one question per thread.

The basic idea in permutations is VERY simple.

Suppose you have four differently colored balls, say red, blue, green, and orange. If you line them up side by side, you get a pattern of colors. How many different patterns are there?

Well I could choose the first ball on the left to be any one of four different colors, right?

Having chosen the first ball on the left, I have three choices for the next ball, correct?

Having chosen the first two balls, I have two choices left for the next ball, don't I?

And for the last ball, I have only 1 possible choice of color.

So the number of possibilities = 4 * 3 * 2 * 1. Do you understand that?

Now this kind of product comes up so many times in counting problems that a special symbol represents it.

4 * 3 * 2 * 1 = 4!.

In general, the definition of this symbol is, assuming n is a non-negative integer:

\(\displaystyle n = 0 \implies n! = 1.\)

\(\displaystyle n \gt 0 \implies n! = n * (n - 1)!.\)

Now see if you can answer pka's post.

Then work on the next problem, and, IN A SEPARATE post, tell us what you got as an answer and your work or show us where you are stuck.