Math Problem Statement
In a card game you are dealt seven cards (click image to enlarge). Determine how many different ways you can fan out your hand.:
Now suppose three of the cards in your hand are Hearts; two of the cards are Clubs; and two of the cards are Spades. Keeping the cards together by their suit, determine how many different ways you can fan out your hand.:
Solution
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Math Problem Analysis
Mathematical Concepts
Permutations
Factorial
Combinatorics
Formulas
P(n) = n! (Permutations of n distinct objects)
3! (Permutations of suits)
3! (Permutations within Hearts)
2! (Permutations within Clubs)
2! (Permutations within Spades)
Theorems
Fundamental Principle of Counting
Suitable Grade Level
Grades 10-12
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