SOLUTION: pleas, solve me 1) if nP5=6720 find n 2) solve equation for n nP3=210 thank you for your helping us

Algebra ->  Permutations -> SOLUTION: pleas, solve me 1) if nP5=6720 find n 2) solve equation for n nP3=210 thank you for your helping us      Log On


   



Question 976741: pleas, solve me
1) if nP5=6720 find n
2) solve equation for n
nP3=210
thank you for your helping us

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
1) if nP5=6720 find n
nP5%22%22=%22%22n%28n-1%29%28n-2%29%28n-3%29%28n-4%29%22%22=%22%226720

n%28n-1%29%28n-2%29%28n-3%29%28n-4%29%22%22=%22%226720

Those 5 factors on the left average to the middle one n-2, 
so the left side isn't far from n-2%29%5E5

So the solution to

%28n-2%29%5E5%22%22=%22%226720 

should be close to the correct answer,

n-2%22%22=%22%22root%285%2C6720%29

n-2%22%22=%22%225.827386917

n%22%22=%22%227.827386917

So we try 8

n%28n-1%29%28n-2%29%28n-3%29%28n-4%29%22%22=%22%226720
8%288-1%29%288-2%29%288-3%29%288-4%29%22%22=%22%226720
8%287%29%286%29%285%29%284%29%22%22=%22%226720
6720%22%22=%22%226720

n = 8
---------------------

2) solve equation for n
nP3=210
nP3%22%22=%22%22n%28n-1%29%28n-2%29

n%28n-1%29%28n-2%29%22%22=%22%22210

These 3 factors on the left average to the middle one n-1, 
so the left side isn't far from n-1%29%5E3

So the solution to

%28n-1%29%5E3%22%22=%22%22210 

should be close to the correct answer,

n-1%22%22=%22%22root%283%2C210%29

n-1%22%22=%22%225.943921953

n%22%22=%22%226.943921953

So we try 7

n%28n-1%29%28n-2%29%22%22=%22%22210
7%287-1%29%287-2%29%22%22=%22%22210
%287%29%286%29%285%29%22%22=%22%22210
210%22%22=%22%22210

n = 7

Edwin