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How many 9 step paths are there from $E$ to $G$ which pass through $F$?

Guest Apr 2, 2015

Best Answer 

 #3
avatar+92805 
+10

Mmm  Well there are 4 ways to get from E to F

 

Now going from F to G

If you horizontal first then there are 4 ways

if you go down1 then across there are 3 ways

if you go down 2 then across there ae 2 ways

if you go all the way down first then there is 1 way.

4+3+2+1=10 ways

 

If that is correct then there would be   4*10=40 ways to go from  E to F to G

Melody  Apr 2, 2015
 #1
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0

Please help me quick. I have atime limit

Guest Apr 2, 2015
 #2
avatar+87303 
+10

The ways to get from E to F =  [1 + 3] !  / [1! * 3!]  = 4!/3!  = 4 ways

Ways to get from F to G  = [3 + 2]! / [3! * 2! ] =   5! / 12 =  120 / 12 = 10 ways

So

4 ways  x  10 ways  = 40 ways to go from E to G  through F 

 

  

CPhill  Apr 2, 2015
 #3
avatar+92805 
+10
Best Answer

Mmm  Well there are 4 ways to get from E to F

 

Now going from F to G

If you horizontal first then there are 4 ways

if you go down1 then across there are 3 ways

if you go down 2 then across there ae 2 ways

if you go all the way down first then there is 1 way.

4+3+2+1=10 ways

 

If that is correct then there would be   4*10=40 ways to go from  E to F to G

Melody  Apr 2, 2015
 #4
avatar+92805 
+5

CPhill and I got the same answer, wonders never cease!

Melody  Apr 2, 2015
 #5
avatar+87303 
+5

I actually can't take much credit for this one.......the answer comes straight from a "formula" supplied by  Nauseated....

For any R x C grid arrangement where R represents the rows and C represents the columns.....the number of distinct paths from one corner of the grid to a diagonally opposite corner is given by :

(R + C ) !   / [R! * C! ]

 

  

CPhill  Apr 2, 2015
 #6
avatar
+5

Minimum amount of steps E -> F -> G is 8, but 9 steps is required.

I.e. E -> F in 4 steps & F -> G in 5 steps, or E -> F in 5 steps & F -> G in 4 steps.

So is 40 ways to go from E to F to G in 8 steps, or did you somehow take that additional step into account?

(I don't have spare time to calculate, so cannot check this.. so just wondering)

Guest Apr 2, 2015
 #7
avatar+92805 
+5

Hi anon, thanks for getting involved - we like that.

However, the minimum number is 9.     5 across and 4 down  

I  don't know where you got 8 from?      :)

 

Hi Chris,

Yes i thought that might be Nauseated's formula,  It is nifty, 

There are so many formuas for so many things i cannot remember them all.

I suppose i should try and organise a file for some of these new ones. 

Melody  Apr 2, 2015

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