• Support PF! Buy your school textbooks, materials and every day products Here!

Permutations help

  • Thread starter LampMan
  • Start date
  • #1
5
0

Homework Statement



prove the following natural numbers n and r.

P(n-1,2) + 3P(n+1,2) = 2(2n^2 + 1) and P(n,r) = P(n-3,r-3)


The Attempt at a Solution



i honestly dont even know what this question is asking. this is a sort of handout of 3 questions our teacher gave us in which we havent ever done any questions like this, its to challenge us, but we also get marked on it, but im drawing blanks.

can i get any sort of start off help? or atleast an explanation on what im trying to achieve
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
Hi LampMan! :smile:

(try using the X2 tag just above the Reply box :wink:)
prove the following natural numbers n and r.

P(n-1,2) + 3P(n+1,2) = 2(2n^2 + 1) and P(n,r) = P(n-3,r-3)
If P(n,r) is the number of ways of chooosing r objects out of n, then the first equation is fairly easy to prove.

But I don't know what the second equation is supposed to be … are you sure you have copied it correctly?
 
  • #3
tiny-tim wrote:

"If P(n,r) is the number of ways of chooosing r objects out of n, then the first equation is fairly easy to prove."

I think P(n,r) is meant to be the number of permutations of r objects taken from n different objects (written [itex]^nP_r[/itex] when I was at school), rather than the number of ways of choosing r objects from n different objects, [itex]^nC_r[/itex], the difference being that each different order of the r selected objects is counted as a different permutation, whereas the order is not relevant for a choice.

If P(n,r) were taken to mean [itex]^nC_r[/itex] as tiny-tim suggestes, the right hand side of the first equation would be double the correct value.

Either way the second equation is invalid. Mabe it should read P(n,r) [itex]\geq[/itex] P(n-3,r-3).
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
250
Hi Martin! :smile:
…I think P(n,r) is meant to be the number of permutations of r objects taken from n different objects (written [itex]^nP_r[/itex] when I was at school), rather than the number of ways of choosing r objects from n different objects, [itex]^nC_r[/itex], the difference being that each different order of the r selected objects is counted as a different permutation, whereas the order is not relevant for a choice.
Yes, you're right, I should have been more precise :redface:

C is the number of ways of choosing in which the order doesn't matter, and P is the number of ways of choosing in which the order matters.

Thanks for the correction. :smile:
 

Related Threads on Permutations help

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
13
Views
4K
Replies
9
Views
867
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
13
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
949
Top