---
id: 6a0dcd03ee4e68698080ef68
title: "Challenge 304: Itinerary Arrangements"
challengeType: 29
dashedName: challenge-304
---

# --description--

Given an array of at least two optional stops for a day trip, return the number of valid itinerary arrangements.

The itinerary always includes `"breakfast"`, `"lunch"`, and `"dinner"`, these will not be passed in as arguments. The optional stops can be placed anywhere in the itinerary, subject to the following rules:

- `"breakfast"` is always first, with at least one stop before `"lunch"`.
- `"lunch"` must appear before `"dinner"`, with at least one stop in between.
- At most, one optional stop may appear after `"dinner"`.

Return the number of valid arrangements.

# --hints--

`get_itinerary_count(["library", "park"])` should return `2`.

```js
({test: () => { runPython(`
from unittest import TestCase
TestCase().assertEqual(get_itinerary_count(["library", "park"]), 2)`)
}})
```

`get_itinerary_count(["library", "park", "arcade"])` should return `18`.

```js
({test: () => { runPython(`
from unittest import TestCase
TestCase().assertEqual(get_itinerary_count(["library", "park", "arcade"]), 18)`)
}})
```

`get_itinerary_count(["library", "park", "arcade", "store"])` should return `120`.

```js
({test: () => { runPython(`
from unittest import TestCase
TestCase().assertEqual(get_itinerary_count(["library", "park", "arcade", "store"]), 120)`)
}})
```

`get_itinerary_count(["library", "park", "arcade", "store", "cafe"])` should return `840`.

```js
({test: () => { runPython(`
from unittest import TestCase
TestCase().assertEqual(get_itinerary_count(["library", "park", "arcade", "store", "cafe"]), 840)`)
}})
```

`get_itinerary_count(["library", "park", "arcade", "store", "cafe", "market", "museum"])` should return `55440`.

```js
({test: () => { runPython(`
from unittest import TestCase
TestCase().assertEqual(get_itinerary_count(["library", "park", "arcade", "store", "cafe", "market", "museum"]), 55440)`)
}})
```

# --seed--

## --seed-contents--

```py
def get_itinerary_count(stops):

    return stops
```

# --solutions--

```py
from math import factorial

def get_itinerary_count(stops):
    n = len(stops)
    return (2 * n - 3) * factorial(n)
```