Cardinality Rules for Dice Rolls

This text discusses how to use cardinality rules to count the number of possible dice rolls. The author gives three examples, each with a different number of dice that have the same value. The author then asks the reader to write a simple formula for the number of possible 104-card double-deck mixes.

Questions

• (a) For how many rolls do exactly two dice have the value 6 and the remaining five dice all have different values?
• (b) For how many rolls do two dice have the same value and the remaining five dice all have different values?
• (c) For how many rolls do two dice have one value, two different dice have a second value, and the remaining three dice a third value?

Answers

• (a) There are 6 * 5 = 30 possible rolls.
• (b) There are 6 * 5 * 4 = 120 possible rolls.
• (c) There are 6 * 5 * 2 = 60 possible rolls.