From 5c4b0aab8eceb5f8b939f98c279f277eab70106e Mon Sep 17 00:00:00 2001
From: Rolv Apneseth <rolv.apneseth@gmail.com>
Date: Sat, 24 Oct 2020 00:58:21 +0100
Subject: [PATCH 1/4] Made improvements to combinations.py

---
 maths/combinations.py | 53 ++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 50 insertions(+), 3 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index fd98992e6c16..8e7b34f3e8c4 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -1,19 +1,66 @@
+"""
+This function will return the total number of different combinations of
+k length which can be made from n values.
+
+Wikipedia page here: https://en.wikipedia.org/wiki/Combination
+
+For doctests, run: `python3 -m doctest -v combinations.py`
+
+Run `python3 combinations.py` for print statements which demonstrate use
+cases for this function.
+"""
 from math import factorial
 
 
-def combinations(n, k):
+def combinations(n: int, k: int) -> int:
     """
+    Returns the number of different combinations of k length which can
+    be made from n values, where n >= k.
+
+    Examples:
     >>> combinations(10,5)
     252
+
     >>> combinations(6,3)
     20
+
     >>> combinations(20,5)
     15504
+
+    >>> combinations(52, 5)
+    2598960
+
+    >>> combinations(0, 0)
+    1
+
+    >>> combinations(-4, -5)
+    Invalid value for n and/or k given.
+    -1
     """
+
+    # If either of the conditions are true, the function is being asked
+    # to calculate a factorial of a negative number, which is not possible
+    if n < k or k < 0:
+        print("Invalid value for n and/or k given.")
+        return -1
     return int(factorial(n) / ((factorial(k)) * (factorial(n - k))))
 
 
 if __name__ == "__main__":
-    from doctest import testmod
 
-    testmod()
+    print(
+        "\nThe number of five-card hands possible from a standard",
+        f"fifty-two card deck is: {combinations(52, 5)}",
+    )
+
+    print(
+        "\nIf a class of 40 students must be arranged into groups of",
+        f"4 for group projects, there are {combinations(40, 4)} ways",
+        "to arrange them.\n",
+    )
+
+    print(
+        "If 10 teams are competing in a Formula One race, there",
+        f"are {combinations(10, 3)} ways that first, second and",
+        "third place can be awarded.\n",
+    )

From 2e8812768336fb071e2a4b0583b00ccf4f42567a Mon Sep 17 00:00:00 2001
From: Rolv Apneseth <rolv.apneseth@gmail.com>
Date: Sat, 24 Oct 2020 21:14:39 +0100
Subject: [PATCH 2/4] Update maths/combinations.py

Co-authored-by: Du Yuanchao <shellhub.me@gmail.com>
---
 maths/combinations.py | 10 +---------
 1 file changed, 1 insertion(+), 9 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index 8e7b34f3e8c4..a5b7ae79b204 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -1,13 +1,5 @@
 """
-This function will return the total number of different combinations of
-k length which can be made from n values.
-
-Wikipedia page here: https://en.wikipedia.org/wiki/Combination
-
-For doctests, run: `python3 -m doctest -v combinations.py`
-
-Run `python3 combinations.py` for print statements which demonstrate use
-cases for this function.
+https://en.wikipedia.org/wiki/Combination
 """
 from math import factorial
 

From f24ceb0688f0bc6836b67e27a0c1a5092c080b09 Mon Sep 17 00:00:00 2001
From: Rolv Apneseth <rolv.apneseth@gmail.com>
Date: Sun, 25 Oct 2020 15:50:24 +0000
Subject: [PATCH 3/4] Function now raises an error when given invalid input

---
 maths/combinations.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/maths/combinations.py b/maths/combinations.py
index a5b7ae79b204..ee3a1878d07e 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -26,15 +26,14 @@ def combinations(n: int, k: int) -> int:
     1
 
     >>> combinations(-4, -5)
-    Invalid value for n and/or k given.
-    -1
+    Traceback (most recent call last):
+    ValueError: Please enter positive integers for n and k where n >= k
     """
 
     # If either of the conditions are true, the function is being asked
     # to calculate a factorial of a negative number, which is not possible
     if n < k or k < 0:
-        print("Invalid value for n and/or k given.")
-        return -1
+        raise ValueError("Please enter positive integers for n and k where n >= k")
     return int(factorial(n) / ((factorial(k)) * (factorial(n - k))))
 
 

From 985d7aae7fe223b000f88806511571c968b7bbe8 Mon Sep 17 00:00:00 2001
From: Du Yuanchao <shellhub.me@gmail.com>
Date: Mon, 26 Oct 2020 14:42:09 +0800
Subject: [PATCH 4/4] Update maths/combinations.py

---
 maths/combinations.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/combinations.py b/maths/combinations.py
index ee3a1878d07e..40f4f7a9f850 100644
--- a/maths/combinations.py
+++ b/maths/combinations.py
@@ -26,6 +26,7 @@ def combinations(n: int, k: int) -> int:
     1
 
     >>> combinations(-4, -5)
+    ...
     Traceback (most recent call last):
     ValueError: Please enter positive integers for n and k where n >= k
     """