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Probability Counting - Ways to Order 4 Cards, 2 Repeats - to Equation (Level 1)

This math topic focuses on developing skills in determining the number of distinct ways to order sets of 4 cards, some of which are repeated, using multiplicative combinations. Students are guided through calculating possible permutations by addressing factorial notation and division to account for repeated items, consistent with introductory principles in probability and statistics. The problems require foundational understanding of the binomial theorem, as it relates to organizing combinations and permutations. Each problem set provides multiple-choice answers formulated in mathematical expressions, enhancing computational and problem-solving skills relevant to probability applications.

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

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Ways to Order 4 Cards, 2 Repeats - to Equation

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

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Probability Counting - Ways to Order 4 Cards, 2 Repeats - to Equation Worksheet

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Math worksheet on 'Probability Counting - Ways to Order 4 Cards, 2 Repeats - to 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 multiplication.
a A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
b A LaTex expression showing 4 times 3 times 2 over 2 times 3 times 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 2 times 2
d A LaTex expression showing 3 times 2 over 2 times 2
e A LaTex expression showing 4 times 3 times 2 over 2 times 2
f A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 2
2
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a multiplication.
a A LaTex expression showing 4 times 3 times 2 over 2 times 3 times 2
b A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2 times 2 times 2
d A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
e A LaTex expression showing 3 times 2 over 2 times 2
f A LaTex expression showing 4 times 3 times 2 over 2 times 2
3
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a multiplication.
a A LaTex expression showing 4 times 3 times 2 over 2 times 4 times 3 times 2
b A LaTex expression showing 3 times 2 over 2 times 2
c A LaTex expression showing 4 times 3 times 2 over 2 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
e A LaTex expression showing 4 times 3 times 2 over 2 times 2
4
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a multiplication.
a A LaTex expression showing 4 times 3 times 2 over 2 times 3 times 2
b A LaTex expression showing 4 times 3 times 2 over 2 times 2
c A LaTex expression showing 3 times 2 over 2 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 2 times 2
e A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
5
How many distinct ways can these cards be ordered? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
b A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 2 times 2 times 2
c A LaTex expression showing 4 times 3 times 2 over 2 times 4 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 2 times 2
e A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 2 times 2
f A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 3 times 2 times 2 times 2
6
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a multiplication.
a A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 2
b A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
c A LaTex expression showing 3 times 2 over 2 times 2
d A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 2
e A LaTex expression showing 4 times 3 times 2 over 2 times 2
7
An svg image showing a math problem
How many distinct ways can these cards be ordered? Show as a multiplication.
a A LaTex expression showing 4 times 3 times 2 over 2 times 2
b A LaTex expression showing 3 times 2 over 2 times 2
c A LaTex expression showing 4 times 3 times 2 over 2 times 4 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
e A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 2
f A LaTex expression showing 5 times 4 times 3 times 2 over 2 times 2