# [Python] Permutations and Combinations Question, programming homework help

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### Question Description

Before you start notes:

• Enter your answers to these questions in the accompanying Python script file `questions.py`. Questions 1–3 require only short pieces of code to calculate or generate the answers, so replace the entries that say `None` with your answers to each part. Question 4 has you completing the implementation of two functions.
• For questions 1–3, a helper function, `fact(n)`, has been included that provides a simpler interface to SciPy’s `factorial` function. Note that the `comb` function will produce real numbers as output instead of integers. The assessment scheme will accept either, as long as the value is correct.
• (HINT): While developing your code, store the result in a variable so that Spyder doesn’t immediately try to display it (since it may be large).
• (HINT): Use the `len()` function to check that your result set is the expected size. If your result, stored in set `s`, is (necessarily) large, then use code like `sorted(s)[:20]` to look at only the first 20 elements of `s`. The use of `sorted()` will often make it easier for you to confirm that it is generating the right entries.
• If your script file takes more than ~3 seconds to run then you’ve probably implemented one of the set comprehensions incorrectly.

QUESTIONS (input your answer to these questions to the corresponding parts in the python file provided):

# Question 1: Permutations

1. How many strings of length three are possible using characters from ‘ATGC’ (characters may be reused)? Write Python code tocalculate the number.
2. Write a set comprehension to generate those strings.
3. How many four-word sentences can be created from the words ‘cat’, ‘bat’, ‘hat’, ‘sat’, ‘fat’, and ‘rat’, using each word at most once? (Most of the sentences won’t make sense.) Write Python code to calculate the number.
4. Write a set comprehension to generate tuples (not single strings) of the different arrangements described in part (c).

# Question 2: Combinations

You should use the definitions of toy droid names and Star Trek species provided in the assignment script in your answers.

1. With the resurgence of Star Wars in the cinemas toy companies are keen to invent new toys for children to collect. They have a series of 16 droids (Star Wars robots) and sell them in mixed packs of four (no pack contains a duplicate droid). How many distinct packs do they sell? Write Python code to calculate the number.
2. Given the droid names defined in the script file, write a set comprehension to generate all compositions of packs of four droids.
3. The various Star Trek television and film series have introduced a large number of different (humanoid) alien species. One of the common narrative devices is to say that a character’s parents are from two different alien species, and hence that character has a blend of characteristics from the two (yes, science fiction can get away with being both horribly racist and ignorant of biology). For example, the popular character Spock is described as having a Human mother and Vulcan father. Your task:Assuming characters can only have two parents, and ignoring which parent is which species, how many different combinations of such ‘blended’ Star Trek characters are possible given the subset of Star Trek species { ‘Bajoran’, ‘Betazoid’, ‘Cardassian’, ‘Human’, ‘Klingon’, ‘Romulan’, ‘Vulcan’ }? Write Python code to calculate the number. Do not directly call `factorial` or `fact` in your solution.
4. Write a set comprehension to generate those combinations. (The answer will be a set of 2-tuples, or pairs.)

# Question 3: You choose which

The following information is used in all parts of this question. Anne has 23 books in her collection at home. They all have short titles: ‘A’, ‘B’, ‘C’, …, ‘W’ (there is a list of these in the assignment script).

1. Anne is going on holiday, but can only take six books with her. What are her options? Write a set comprehension to generate them all.
2. All of Anne’s books fit on a single shelf. How many different ways can she arrange them? Write Python code to calculate the number.
3. Anne sometimes likes to reread books, and may even reread a book she has just finished. What are the possible sequences of book titles of the last three books she has read? Write a set comprehension to generate the alternatives.
4. Write Python code to calculate how many such sequences there are. (Do not use the `len` function on your previous answer.)

# Question 4: Lovers of anagrams know words are mightier than the sword

An anagram is a word whose letters, when rearranged, form another word. They are a common feature of cryptic crosswords, but you do not need to know how to solve a cryptic crossword to solve this question. An anagram solver finds the alternative arrangements of a word’s letters that represent valid words. Your task is to write the two components of a basic anagram solver: the first part generates the set of all possible permutations of the letters in a given word; the second part restricts this set to contain only those permutations that are valid words.

There are two stub functions for you to complete:

1. `word_perms(word)`: should generate and `return` all permutations of the letters in the string represented by `word` (each permutation will be a single string, not a tuple). It will probably be one line of code.
2. `anagrams(word)`: should `return` a set of all the permutations of the letters in `word` that are valid (that is, that appear in one of the collections of words described below), including the original word. The input can be assumed to be in lower case.
Not all solutions to this task will receive full marks; an ideal solution will look very short, but still be readable.

The assignment script file contains code to load collections of words of different lengths (between 2 and 10) into two Python`dict`ionaries, one that holds the words in sorted lists and another that holds them in sets. To use the list of words of length n, use`word_lists[n]`, whereas to use the set of words of length n, use `word_sets[n]` (you will probably not have a variable called `n` but an expression instead). You do not necessarily have to use both of these. Select whichever you believe is best-suited to the task.

In order for these words to be loaded in your program you must download and unzip the file containing the words, `words.2-10.txt`, that accompanies this document.

To test `word_perms`, call it with very short words for which you can enumerate all the possible permutations. To test `anagrams` try it on the word ‘lovers’. Other good words you could try include ‘alerts’, ‘heart’, ‘parsec’ and ‘spare’.

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