Remove type cast in combinations algorithm

DIRECTORY.md

@@ -55,6 +55,7 @@
   * [Modular Division](blockchain/modular_division.py)
 
 ## Boolean Algebra
+  * [And Gate](boolean_algebra/and_gate.py)
   * [Norgate](boolean_algebra/norgate.py)
   * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py)
 
@@ -948,6 +949,7 @@
   * [Quantum Random](quantum/quantum_random.py)
   * [Ripple Adder Classic](quantum/ripple_adder_classic.py)
   * [Single Qubit Measure](quantum/single_qubit_measure.py)
+  * [Superdense Coding](quantum/superdense_coding.py)
 
 ## Scheduling
   * [First Come First Served](scheduling/first_come_first_served.py)
@@ -1037,7 +1039,6 @@
   * [Can String Be Rearranged As Palindrome](strings/can_string_be_rearranged_as_palindrome.py)
   * [Capitalize](strings/capitalize.py)
   * [Check Anagrams](strings/check_anagrams.py)
-  * [Check Pangram](strings/check_pangram.py)
   * [Credit Card Validator](strings/credit_card_validator.py)
   * [Detecting English Programmatically](strings/detecting_english_programmatically.py)
   * [Dna](strings/dna.py)
@@ -1046,6 +1047,8 @@
   * [Indian Phone Validator](strings/indian_phone_validator.py)
   * [Is Contains Unique Chars](strings/is_contains_unique_chars.py)
   * [Is Palindrome](strings/is_palindrome.py)
+  * [Is Pangram](strings/is_pangram.py)
+  * [Is Spain National Id](strings/is_spain_national_id.py)
   * [Jaro Winkler](strings/jaro_winkler.py)
   * [Join](strings/join.py)
   * [Knuth Morris Pratt](strings/knuth_morris_pratt.py)
@@ -1090,6 +1093,7 @@
   * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py)
   * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py)
   * [Get Imdbtop](web_programming/get_imdbtop.py)
+  * [Get Top Billioners](web_programming/get_top_billioners.py)
   * [Get Top Hn Posts](web_programming/get_top_hn_posts.py)
   * [Get User Tweets](web_programming/get_user_tweets.py)
   * [Giphy](web_programming/giphy.py)

maths/combinations.py

@@ -35,24 +35,24 @@ def combinations(n: int, k: int) -> int:
     # to calculate a factorial of a negative number, which is not possible
     if n < k or k < 0:
         raise ValueError("Please enter positive integers for n and k where n >= k")
-    return int(factorial(n) / ((factorial(k)) * (factorial(n - k))))
+    return factorial(n) // (factorial(k) * factorial(n - k))
 
 
 if __name__ == "__main__":
 
     print(
-        "\nThe number of five-card hands possible from a standard",
-        f"fifty-two card deck is: {combinations(52, 5)}",
+        "The number of five-card hands possible from a standard",
+        f"fifty-two card deck is: {combinations(52, 5)}\n",
     )
 
     print(
-        "\nIf a class of 40 students must be arranged into groups of",
+        "If 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",
+        "third place can be awarded.",
     )