Homework Help: Permutations help

LampMan · Mar 29, 2010

1. The problem statement, all variables and given/known data

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)

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

tiny-tim · Mar 29, 2010

Hi LampMan!

(try using the X² tag just above the Reply box )

LampMan said: ↑

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?

Martin Rattigan · Mar 30, 2010

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).

tiny-tim · Mar 30, 2010

Hi Martin!

Martin Rattigan said: ↑

…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 …

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.

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Homework Help: Permutations help

LampMan

tiny-tim

Martin Rattigan

tiny-tim