faizel wants to travel from his house to the hardware store that is six blocks east and five blocks south of his home. If he walks east and south, how many different different routes can he follow from his house to the store?

Can somebody help me setup this question? I don't understand it

You must have a map that shows the streets he could follow from his house to the store.

Should I create a grid 6 by 5? :S

Sure! Let's break down the problem step by step.

1. Faizel's house is represented as a starting point. Let's mark it as "H".
2. The hardware store is six blocks east and five blocks south of his home. Let's mark it as "S".
So the location of the hardware store is six blocks east and five blocks south of "H".
3. Faizel wants to walk from his house to the hardware store, moving only east and south.
4. The task is to find the number of different routes Faizel can follow to reach the hardware store.

To visualize this, we can create a grid and mark Faizel's house and the hardware store on it. Each block will be represented by a rectangle. Here's an example of what it may look like:

```
-------------------------------
| | | | | |
| | | | | |
| H | | | | |
| | | | | |
| | | | | |
-------------------------------
| | | | | |
| | | | | |
| | | | | S |
| | | | | |
| | | | | |
-------------------------------
```

In this grid, Faizel's house (H) is located in the top left corner, and the hardware store (S) is located six blocks to the right and five blocks down.

To find the number of different routes, we can use the concept of permutations. Since Faizel can only move east and south, he has to take a total of 11 steps (6 steps east and 5 steps south) to reach the hardware store.

The number of different routes can be calculated using the formula for permutations:

P(n, k) = n! / (n-k)!

Where n is the total number of steps and k is the number of steps in one direction (either east or south).

In this case, n = 11 and k = 6 (since Faizel can take any of the 6 available steps either east or south).

Plugging these values into the formula, we get:

P(11, 6) = 11! / (11-6)!

Calculating this, we find:

P(11, 6) = 11! / 5!
= (11 * 10 * 9 * 8 * 7 * 6!) / 5!
= (11 * 10 * 9 * 8 * 7) / 5!
= 27720 / 120
= 231

So there are 231 different routes Faizel can follow from his house to the hardware store.

Sure! Let's break down the question and set it up step by step.

1. Faizel wants to travel from his house to the hardware store.
2. The hardware store is six blocks east and five blocks south of his home.
3. He can only travel east and south.

To visualize this, you can think of a grid or a map. Let's assume each block represents one unit.

First, draw a starting point for Faizel's house. Now, he needs to travel six blocks east and five blocks south. Each time he moves east, he will move one unit to the right, and each time he moves south, he will move one unit downwards.

The question asks how many different routes he can take. To determine this, we can use the concept of permutations.

To reach the hardware store, Faizel needs to take a total of 6 + 5 = 11 steps (6 east steps + 5 south steps).

Now, we need to calculate the number of different ways he can arrange these steps.

Since he can only move east or south, the order matters. We can think of this as a permutation problem, where each east step and each south step is considered different.

To calculate the number of permutations, we can use the formula for factorial: n! (n factorial).

In this case, n = total number of steps = 11.

So, the number of different routes Faizel can take is 11!.

To calculate 11!, we multiply all the numbers from 1 to 11 together:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Now you can multiply these numbers to find the answer, which will give you the total number of different routes Faizel can take from his house to the hardware store.