anonymous
  • anonymous
im trying to solve P(n,3) = 2(n-1 P 3) using permutations
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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hartnn
  • hartnn
and where are u stuck ?
anonymous
  • anonymous
how to solve each side to get an answer
hartnn
  • hartnn
you know the definition of \(\large _nP^r\) ?

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hartnn
  • hartnn
sorry, \(\large ^nP_r\)
anonymous
  • anonymous
i know its permutations
hartnn
  • hartnn
so, \(\huge \dfrac{n!}{(n-3)!}=2 \times \dfrac{(n-1)!}{(n-4)!}\) did u get till here ?
anonymous
  • anonymous
yes, i don't know how to show to solve each side from there
hartnn
  • hartnn
use the fact that \(\huge n!=n(n-1)!\) and \(\huge n!=n(n-1)!=n(n-1)(n-2)!\) and so on...
anonymous
  • anonymous
how do i solve the right side of the right side f the equation when its multiplied by 2?
hartnn
  • hartnn
\(\huge \dfrac{n(n-1)!}{(n-3)(n-4)!}=2 \times \dfrac{(n-1)!}{(n-4)!}\) did you get what i did ?
hartnn
  • hartnn
numerator of left is obvious, for denominator, \(\large (n-3)! = (n-3)(n-3-1)! = (n-3)(n-4)!\) got this ?
anonymous
  • anonymous
i dont understand why the denominator is like that
hartnn
  • hartnn
\(\large a!=a(a-1)!\) this is standard, right ? now just replace a by n-3
anonymous
  • anonymous
ok
hartnn
  • hartnn
now what gets cancelled ?
anonymous
  • anonymous
i dont know
hartnn
  • hartnn
now you got this right ? \(\huge \dfrac{n(n-1)!}{(n-3)(n-4)!}=2 \times \dfrac{(n-1)!}{(n-4)!}\) how can you simplify this ? notice that some terms are getting cancelled!
anonymous
  • anonymous
does the (n-1)! on the tops cancel out and the (n-4)! on the bottoms cancell out?
hartnn
  • hartnn
YES! and what remains ??
anonymous
  • anonymous
\[\frac{ n }{ (n-3) } = 2\]
hartnn
  • hartnn
yes, isn't this easy to solve ? (NOTE : since we are cancelling (n-1)! , which can be 0, we need to account for n-1 =0 and so, n=1 is a solution)
hartnn
  • hartnn
and since we cancelled, (n-4) ! also, solve (n-4)! = 0, n=.... ?, ...?
hartnn
  • hartnn
are u getting all this ?
anonymous
  • anonymous
so becasue it equaled the fraction, then it goes down to 2(n-3)=n?
anonymous
  • anonymous
and then it goes to 2n-6=n ?
hartnn
  • hartnn
yes, continue, n=... ?
anonymous
  • anonymous
2n=n+6 ?
anonymous
  • anonymous
is that right?
anonymous
  • anonymous
or is it n =6
anonymous
  • anonymous
thanks for your help!
hartnn
  • hartnn
n=6 is correct! :) welcome ^_^ and \(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

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