Permutation question (math) [ ]

[F|234K]

permutation question (math) [urgent]

image here

please solve this problem for me. the correct answer is c.

i put 10!/(4!6!), then i know i am suppose to divide/subtract something, but i don't know what. (i have never done this kind of problem before.)

 

[JamesU]

hell I am stumped...

 

[BicycleTree]

You can just add up the ways to get to each vertex. Here are the first few (period represents a vertex, number before each vertex is the number of ways to get to it):

1. 1. 1. 1. 1.  .  .
1. 2. 3. 4. 5.  .  .
1. 3. 6.        .  .
1. 4.10.  .  .  .  .
 .  .  .  .  .  .  .

See what I'm doing and why?

 

[F|234K]

somebody please help

 

[F|234K]

but how u going to get the numbers for the dots in the park!

i did try to solvei t using pascal triangle thing...but i got stuck on the park thing...

 

[BicycleTree]

There are no dots in the park. And it's not exactly Pascal's triangle because of the park. Here's a hint (some more vertexes filled in):

1. 1. 1. 1. 1.  .  .
1. 2. 3. 4. 5. 6.  .
1. 3. 6.       6.  .
1. 4.10.10.  .  .  .
 .  .  .  .  .  .  .

 

[whozum]

Im guessing the park is considered as one big square.

 

[BicycleTree]

No, the park is considered a blank. The number of ways to get to any vertex is equal to the sum of the number of ways to get to any of the immediately preceding vertices.

 

[F|234K]

why u have a 10 after the 10? how the get the second 10?

 

[BicycleTree]

For example take the first 10 you get, at vertex (4, 3) by row, column. At vertex (3, 3) you have a 6, and at vertex (4, 2) you have a 4. You can get to the 10 one of two ways: through (3, 3) by going south, and through (4, 2) by going east. There are 6 ways to get to (3, 3) so there are 6 ways to get to (3, 3) and then go south. There are 4 ways to get to (4, 2) so there are 4 ways to get to (4, 2) and then go east. So you have 4 ways + 6 ways = 10 ways for vertex (4, 3).

If a vertex only has one other vertex leading into it--say the other vertex has 7 ways to get to it--then how many ways can you get to that second vertex?

 

[F|234K]

oh...i think i got it...thanks for this "If a vertex only has one other vertex leading into it--say the other vertex has 7 ways to get to it--then how many ways can you get to that second vertex?"

again..thanks a lot!