We are to solve for n

Please verify

P(n,2)=15

My solution for this problem

By factoting

n(n-1) = 15

n=15 ; n= 16

Another Problem

P(n,5) = 20 P(n,3)

I have no idea how to do it

Hoping for replies, thanks

Printable View

- Jan 13th 2009, 03:43 AMImKoA Permutation Problem-Urgent
We are to solve for n

Please verify

**P(n,2)=15**

My solution for this problem

By factoting

*n(n-1) = 15*

n=15 ; n= 16

Another Problem

**P(n,5) = 20 P(n,3)**

I have no idea how to do it

Hoping for replies, thanks - Jan 13th 2009, 03:52 AMGrandadPerms and coms
- Jan 13th 2009, 04:44 AMImKo
For question number 2

How many answers should it have?Should it have 2? or 1 only? - Jan 13th 2009, 04:47 AMIsomorphism
- Jan 13th 2009, 04:50 AMImKo
Wait here is what I got for question number 2

n=23 or n=24 Is that correct?Basing from the solution provided

And what should be the reason for me to remove one of them in order for it to be only one answer? - Jan 13th 2009, 05:05 AMIsomorphism
If we are still talking about "

, then both your answers are wrong.Didnt the problem reduce to solving the quadratic ?(As shown by Grandad...)**P(n,5) = 20 P(n,3)"**

. Solve this quadratic...

Always verify your answers by substituting it back in the original equation and verify if your answer is right... - Jan 13th 2009, 05:21 AMImKo
Oh My mistake!! Sorry

so using quadratic formula I got

n = (7 + sqrt17 ) / 2 or n = (7 - sqrt17) / 2

Is that right?

Now which should I eliminate - Jan 13th 2009, 05:29 AMmr fantastic
You should have realised that n is a

**positive integer**therefore:

1. Your solutions to the quadratic for n are clearly wrong.

2. The answer to the question*Which of the two correct solutions to the quadratic equation should I eliminate?*is implied by the word in red ..... - Jan 13th 2009, 05:37 AMImKo
Oh! I forgot that the other one is negative, sorry

Is my last solution correct already? - Jan 13th 2009, 05:38 AMGrandadQuadratics
Hello ImKo -

I really think you need to do some work on solving quadratic equations. Your answers using the quadratic formula were incorrect, because you missed a minus sign. But before using the formula, you should always try to factorise - and is one of the easiest quadratic expressions to factorise.

Can you do it?

It will look like this:

This will give you two possible values of , only one of which is appropriate - see mr fantastic's hint.

Grandad

- Jan 13th 2009, 05:45 AMImKo
Sorry I'm a bit careless on solving equations and usually miss the easier approach.. Thanks allot

so the answer would be n = -1 or n = 8

then n = 8 ? - Jan 13th 2009, 05:50 AMGrandadPermutations