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Probability Counting - Ways to Order 5 Cards, 2 Repeats - to Factorial Equation (Level 1)

This math topic focuses on probability calculations involving the arrangement of five cards with repeated elements. It covers how to solve problems by expressing the number of distinct ways to order these cards in factorial notation, involving division of factorials to account for repeated elements. The problems are set within the broader context of probability and statistics, introducing binomial notation. The questions progressively address different scenarios of repetition and permutation, with answers provided as multiple-choice options displayed in LaTeX format. This topic helps develop skills in combinatorial reasoning and understanding factorial calculations relating to probability concepts.

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

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Ways to Order 5 Cards, 2 Repeats - to Factorial Equation

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


How many distinct ways can these cards be ordered? Show as a factorial.

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Probability Counting - Ways to Order 5 Cards, 2 Repeats - to Factorial Equation Worksheet

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Math worksheet on 'Probability Counting - Ways to Order 5 Cards, 2 Repeats - to Factorial Equation (Level 1)'. Part of a broader unit on 'Probability and Statistics - Binomial Notation Intro' Learn online: app.mobius.academy/math/units/probability_and_statistics_probability_with_binomial_notation_intro/
1
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 5! times 0!
b A LaTex expression showing 6! over 2! times 3!
c A LaTex expression showing 5! over 3! times 3!
d A LaTex expression showing 6! over 3! times 2! times 3!
e A LaTex expression showing 4! over 2! times 3!
f A LaTex expression showing 5! over 2! times 3!
2
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 3! times 2!
b A LaTex expression showing 3! over 3! times 2!
c A LaTex expression showing 5! over 5! times 2!
d A LaTex expression showing 7! over 3! times 2!
e A LaTex expression showing 5! over 3! times 4!
f A LaTex expression showing 5! over 5! times 0!
3
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 2! times 2!
b A LaTex expression showing 3! over 2! times 2!
c A LaTex expression showing 7! over 2! times 2!
d A LaTex expression showing 5! over 5! times 0!
e A LaTex expression showing 5! over 3! times 2!
f A LaTex expression showing 6! over 2! times 2!
4
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 3! times 2!
b A LaTex expression showing 5! over 3! times 4!
c A LaTex expression showing 5! over 5! times 0!
d A LaTex expression showing 7! over 2! times 3! times 2!
e A LaTex expression showing 6! over 3! times 2!
5
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 2! times 4!
b A LaTex expression showing 5! over 5! times 0!
c A LaTex expression showing 5! over 2! times 3!
d A LaTex expression showing 4! over 2! times 3!
e A LaTex expression showing 5! over 2! times 5!
6
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 5! over 2! times 4!
b A LaTex expression showing 7! over 2! times 2! times 3!
c A LaTex expression showing 5! over 2! times 5!
d A LaTex expression showing 7! over 2! times 3!
e A LaTex expression showing 5! over 2! times 3!
f A LaTex expression showing 5! over 5! times 0!
7
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a factorial.
a A LaTex expression showing 3! over 2! times 2!
b A LaTex expression showing 5! over 2! times 2!
c A LaTex expression showing 5! over 5! times 0!
d A LaTex expression showing 6! over 2! times 2!
e A LaTex expression showing 5! over 2! times 3!
f A LaTex expression showing 5! over 3! times 2!