Combinations

• How to Find the Probability of Selecting One Student from Each of Three Cities
  For a random group of three drawn without replacement from a combined pool, divide the product of the three city counts by the number of possible groups.
• 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 Combinations Are Possible with Limited Repetitions?
  Count unordered selections of k items from n types with per-type limits using a generating function or an inclusion-exclusion formula.
• 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 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.