Counting

• 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 to Count Elements Divisible by Exactly Two of Three Numbers
  To count elements divisible by exactly two of three divisors, add the three pairwise counts and subtract three times the count divisible by all three.
• 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.