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

This math topic revolves around calculating the different ways to order a set of five cards, some of which may be repeated, using factorial notation. It falls under the broader category of probability and statistics focusing specifically on factorials to determine permutations of items where order matters. The questions require the students to analyze a given situation, invoking their knowledge of factorials to provide solutions in the form of distinct ordering possibilities. The equations involved typically consist of factorials divided by the product of factorials, reflecting the constraints posed by identical items (repeats) among the cards.

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

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Ways to Order 5 Cards, 1 Repeat - to Factorial Equation

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

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Probability Counting - Ways to Order 5 Cards, 1 Repeat - to Factorial Equation Worksheet

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Math worksheet on 'Probability Counting - Ways to Order 5 Cards, 1 Repeat - to Factorial Equation (Level 1)'. Part of a broader unit on 'Probability and Statistics - Probability with Factorials Practice' Learn online: app.mobius.academy/math/units/probability_and_statistics_probability_with_factorials_practice/
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 2!
b A LaTex expression showing 5! over 3!
c A LaTex expression showing 3! over 2!
d A LaTex expression showing 5! over 4!
e A LaTex expression showing 5! over 5! times 0!
f A LaTex expression showing 5! over 2! times 2!
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 6! over 2! times 3!
b A LaTex expression showing 6! over 3! times 3!
c A LaTex expression showing 5! over 5! times 0!
d A LaTex expression showing 6! over 3!
e A LaTex expression showing 5! over 5!
f A LaTex expression showing 5! over 3!
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 7! over 2!
b A LaTex expression showing 5! over 5! times 0!
c A LaTex expression showing 5! over 2! times 2!
d A LaTex expression showing 5! over 2!
e A LaTex expression showing 5! over 2! times 3!
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 5! times 0!
b A LaTex expression showing 5! over 2! times 3!
c A LaTex expression showing 5! over 2!
d A LaTex expression showing 3! over 2!
e A LaTex expression showing 5! over 4!
f A LaTex expression showing 6! over 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 3! times 2!
b A LaTex expression showing 5! over 3!
c A LaTex expression showing 6! over 3!
d A LaTex expression showing 7! over 3!
e A LaTex expression showing 3! over 3!
f A LaTex expression showing 5! over 5! times 0!
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 5! times 0!
b A LaTex expression showing 7! over 4! times 2!
c A LaTex expression showing 5! over 2!
d A LaTex expression showing 3! over 2!
e A LaTex expression showing 6! over 2!
f A LaTex expression showing 7! over 2!
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 5! over 5! times 0!
b A LaTex expression showing 7! over 3! times 3!
c A LaTex expression showing 6! over 2! times 3!
d A LaTex expression showing 5! over 3!
e A LaTex expression showing 5! over 3! times 3!