Permutation question (math) [ ]

In summary, the conversation is about a permutation question in math, where the correct answer is C. The person is stumped and asks for help in solving the problem. Another person suggests adding up the ways to get to each vertex, using a hint and filling in some of the vertexes. They clarify that the park is considered a blank and explain how to get the numbers for the dots in the park. Finally, they answer a question about the number of ways to get to a second vertex with only one other vertex leading into it.
  • #1
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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.)
 
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  • #2
hell I am stumped...
 
  • #3
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):
Code:
1. 1. 1. 1. 1.  .  .
1. 2. 3. 4. 5.  .  .
1. 3. 6.        .  .
1. 4.10.  .  .  .  .
 .  .  .  .  .  .  .

See what I'm doing and why?
 
  • #4
somebody please help
 
  • #5
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...
 
  • #6
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):
Code:
1. 1. 1. 1. 1.  .  .
1. 2. 3. 4. 5. 6.  .
1. 3. 6.       6.  .
1. 4.10.10.  .  .  .
 .  .  .  .  .  .  .
 
  • #7
Im guessing the park is considered as one big square.
 
  • #8
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.
 
  • #9
why u have a 10 after the 10? how the get the second 10?
 
  • #10
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?
 
  • #11
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 alot!
 

1. What is a permutation?

A permutation is an arrangement of objects in a specific order. It is often denoted by the symbol "P" and is used in combinatorics and probability.

2. How do you calculate the number of permutations?

The number of permutations can be calculated using the formula n! / (n-r)! where n is the total number of objects and r is the number of objects being chosen for the permutation.

3. What is the difference between a permutation and a combination?

A permutation takes into account the order of the objects, while a combination does not. In a combination, the order does not matter, whereas in a permutation, the order does matter.

4. Can a permutation have repetitions?

Yes, a permutation can have repetitions. This is known as a repeated permutation and is used when there are repeated objects in the set.

5. How are permutations used in real life?

Permutations are used in a variety of real-life scenarios, such as in statistics to calculate probabilities, in coding to create unique combinations of characters, and in music to create different melodies and chord progressions.

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