freecodecamp--freecodecamp/curriculum/challenges/english/blocks/daily-coding-challenges-python/6a0dcd03ee4e68698080ef68.md

id, title, challengeType, dashedName

id	title	challengeType	dashedName
6a0dcd03ee4e68698080ef68	Challenge 304: Itinerary Arrangements	29	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.

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

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

({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.

({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.

({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.

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

--seed--

--seed-contents--

def get_itinerary_count(stops):

    return stops

--solutions--

from math import factorial

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