Question

Solve for n

Answer 1

\[_nP_6=5(_nP_5)\]

Answer 2

is this algebra 2?

Answer 3

First write these in terms of factorials

Answer 4

remember that:\[_nP_r=\frac{n!}{(n-r)!}\]

Answer 5

ya @osamabinswaggin

Answer 6

i got tht @asnaseer

Answer 7

so where exactly are you stuck on this?

Answer 8

HINT: \((n-5)!=(n-5)(n-6)(n-7)...(3)(2)(1)=(n-5)(n-6)!\)

Answer 9

do i just plug in what i know?

Answer 10

and where does the 5 outside of the (nP_5) come from??

Answer 11

it is just a multiplying factor, e.g.:\[Q\times_nP_r=\frac{Q\times n!}{(n-r)!}\]

Answer 12

so wouldnt r be 25 then?

Answer 13

\[n!\div(n-r)!=5n!\div(5n-30)!\]

Answer 14

lets take one term at a time.

what is:\[_nP_6=?\]in terms of factorials?

Answer 15

n!/(n-6)!

Answer 16

good, now what is:\[_nP_5=?\]in terms of factorials?

Answer 17

n!/(n-5)!

Answer 18

great. your equation is therefore:\[_nP_6=5\left(_nP_5\right)\]\[\therefore \frac{n!}{(n-6)!}=5\left(\frac{n!}{(n-5)!}\right)=\frac{5\times n!}{(n-5)!}\]

Answer 19

the \(n!\) terms on both sides can be cancelled out

Answer 20

ohh ok gotcha

Answer 21

then use the hint I gave you earlier and you should be able to solve this fairly quickly :)

Answer 22

isnt it still 5/(n-6)(n-5) ?

Answer 23

how did you get that?

Answer 24

multiplying both equations

Answer 25

please use the drawing tool to show your steps if you cannot type in latex

Answer 26

\[n!(n-5)!=(n-6)!(5\times n!) \]

Answer 27

ya idk

Answer 28

correct so far :)

now you can cancel the \(n!\) from both sides

Answer 29

leaving you with:\[(n-5)!=5(n-6)!\]

Answer 30

then use the fact that:\[(n-5)!=(n-5)(n-6)!\]and you get:\[(n-5)(n-6)!=5(n-6)!\]now you can cancel out the \((n-6)!\) terms from both sides

Answer 31

where did u get the (n-5) on the right side?

Answer 32

\((n-5)!=(n-5)(n-6)(n-7)...(3)(2)(1)=(n-5)[(n-6)(n-7)...(3)(2)(1)]\)
\(=(n-5)[(n-6)!]\)

Answer 33

oh ok

Answer 34

e.g.\[8!=8*7*6*5*4*3*2*1=8*[7*6*5*4*3*2*1]=8*7!\]

Answer 35

ohh yea I get it now

Answer 36

good - so hopefully you can now solve the equation you were given?

Answer 37

n=10?

Answer 38

perfect! :)

Answer 39

thank you so much!

Answer 40

yw :)

Answer 41

i completely forgot about this...I went off doing other things and lost the medal *cries*