Permutations

• When Should You Use nPr or nCr?
  Use nPr when order matters and nCr when it does not. Learn how replacement changes the count and how to use these counts in probability.
• How Many Numbers Greater Than 1000 Can 1, 1, 2, 2, 3 Form?
  Using each supplied digit at most once, there are 60 distinct numbers greater than 1000: 30 four-digit numbers and 30 five-digit numbers.
• How Many Outcomes Are Possible in a Three-Team Round Robin?
  In a round robin where three teams each play once and a game can be won by either team or drawn, there are 27 outcome combinations.
• How Many Ways Can Men and Women Sit Around a Table with No Adjacent Men?
  For n distinct men and k distinct women seated up to rotation, count the arrangements by placing women first and filling separate gaps.
• How Many Ways Are There to Eat Lunch?
  There is no single count without a menu and rules. Define the lunch choices, then use the product rule, sum rule, or permutations as needed.
• How Many Words Can Be Formed Using 2 Vowels and 3 Consonants?
  Choose 2 of the 4 vowels and 3 of the 5 consonants, then arrange all 5 distinct letters: the total is 7,200 words.