Permutation Questions

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?

pkolla90 said:

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.

Click to expand...

Being new to the forum, you should the post titled "Read Before Posting!". Including

Don't post a list of homework problems. Please show us any work you have done towards answering the problem, and try to explain what specifically is giving you trouble. Also, please try to limit the number of questions you ask to a reasonable number per day. There's no exact limit, but try to be polite and not abuse the service.

and

Show all of your work. If you've shown no work at all, the tutors may assume that you're needing help getting started, and may suggest only how to do the first step. Even if you're asking only about the very end of the solution process, still include all of your intermediate steps. Errors may have occurred earlier than you'd realized; correcting part (b) may clear up your confusion on part (d).

We are not here to do your work for you, but rather to guide you by checking your work and giving suggestions.

1a) the 2 engineers are accounted for, so you only have to consider the remaining 8.
1b) arrange the other 5, then count how many places the 5 mathematicians could be inserted in the line
1c) I suspect the "or" means "either or both"

DrPhil said:

Being new to the forum, you should the post titled "Read Before Posting!". Including

Don't post a list of homework problems. Please show us any work you have done towards answering the problem, and try to explain what specifically is giving you trouble. Also, please try to limit the number of questions you ask to a reasonable number per day. There's no exact limit, but try to be polite and not abuse the service.

and

Show all of your work. If you've shown no work at all, the tutors may assume that you're needing help getting started, and may suggest only how to do the first step. Even if you're asking only about the very end of the solution process, still include all of your intermediate steps. Errors may have occurred earlier than you'd realized; correcting part (b) may clear up your confusion on part (d).

We are not here to do your work for you, but rather to guide you by checking your work and giving suggestions.

1a) the 2 engineers are accounted for, so you only have to consider the remaining 8.
1b) arrange the other 5, then count how many places the 5 mathematicians could be inserted in the line
1c) I suspect the "or" means "either or both"

Click to expand...

Of course, this poster has already been told to read Read Before Posting in the duplicate of this post under Advanced Math. He has also been given some hints on how to do such problems.