Probability Counting

Choose N Cards from M, Count of Total Outcomes - To Factorial Equation (Level 1)

This math topic focuses on understanding and applying the principles of probability concerning combinations. It involves calculating the number of ways to select N cards from a group of M cards using factorial notation. The problems guide students in solving combination queries using formulas like \(\frac{n!}{r!(n-r)!}\), where \(n\) represents the total number of items, and \(r\) represents the number of items to choose. Each question requires expressing the solution as a factorial, reinforcing the student's familiarity with both combination concepts and factorial mathematical operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Probability Counting - Choose N Cards from M, Count of Total Outcomes - To Factorial Equation Worksheet

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Probability Counting - Choose N Cards from M, Count of Total Outcomes - To Factorial Equation
1
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 7! over 4! times 3!
b A LaTex expression showing 5! over 4! times 1!
c A LaTex expression showing 5! over 2! times 3!
d A LaTex expression showing 2! over 5! times 3!
e A LaTex expression showing 5! over 3!
2
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 5! over 3!
b A LaTex expression showing 7! over 2! times 5!
c A LaTex expression showing 3! over 3! times 0!
d A LaTex expression showing 5! over 2! times 3!
e A LaTex expression showing 2! over 5! times 3!
3
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 2! over 5! times 3!
b A LaTex expression showing 5! over 3!
c A LaTex expression showing 3! over 3! times 0!
d A LaTex expression showing 5! over 2! times 3!
4
An svg image showing a math problem
How many total ways can 3 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 3! over 2! times 1!
b A LaTex expression showing 4! over 2! times 2!
c A LaTex expression showing 5! over 3! times 2!
d A LaTex expression showing 5! over 2!
5
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 5! over 3!
b A LaTex expression showing 2! over 5! times 3!
c A LaTex expression showing 5! over 2! times 3!
d A LaTex expression showing 7! over 4! times 3!
6
An svg image showing a math problem
How many total ways can 3 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 3! over 5! times 2!
b A LaTex expression showing 3! over 3! times 0!
c A LaTex expression showing 5! over 2!
d A LaTex expression showing 5! over 3! times 2!
7
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 5! over 3! times 2!
b A LaTex expression showing 7! over 2! times 5!
c A LaTex expression showing 4! over 2! times 2!
d A LaTex expression showing 6! over 2! times 4!
e A LaTex expression showing 6! over 4!
f A LaTex expression showing 2! over 6! times 4!
8
An svg image showing a math problem
How many total ways can 2 cards be drawn from this set? Show as a factorial.
a A LaTex expression showing 7! over 2! times 5!
b A LaTex expression showing 7! over 5!