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

This math topic revolves around the practice of calculating permutations, especially focusing on problems that involve ordering groups of cards with repetitions. It involves the investigative use of factorial mathematics to determine how many distinct ways cards can be arranged, translating these scenarios into multiplicative equations. The material aligns with broader studies in probability and statistics, particularly emphasizing skills with factorial operations used in evaluating permutations and combinations. Each question proposes different scenarios for arranging cards, asking the learner to represent these permutations through specific equations.

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

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Ways to Order 4 Cards, 1 Repeat - to 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 multiplication.

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Probability Counting - Ways to Order 4 Cards, 1 Repeat - to Equation Worksheet

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Math worksheet on 'Probability Counting - Ways to Order 4 Cards, 1 Repeat - to 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 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 4 times 3 times 2
c A LaTex expression showing 4 times 3 times 2 over 2
d A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
2
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 6 times 5 times 4 times 3 times 2 over 2 times 3 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 5 times 4 times 3 times 2 over 3 times 2 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 3 times 2
e A LaTex expression showing 4 times 3 times 2 over 2 times 3 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 3 times 2 over 3 times 2
b A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 2
c A LaTex expression showing 4 times 3 times 2 over 5 times 4 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 3 times 2
e A LaTex expression showing 4 times 3 times 2 over 3 times 2 times 3 times 2
f A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
4
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 4 times 3 times 2 over 3 times 2 times 3 times 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 3 times 2
e A LaTex expression showing 4 times 3 times 2 over 5 times 4 times 3 times 2
f A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 3 times 2 times 3 times 2
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 6 times 5 times 4 times 3 times 2 over 2 times 3 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 3 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
e A LaTex expression showing 4 times 3 times 2 over 3 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 2 times 3 times 2
b A LaTex expression showing 4 times 3 times 2 over 2 times 2
c A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2
d A LaTex expression showing 4 times 3 times 2 over 2
e A LaTex expression showing 3 times 2 over 2
f A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
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 4 times 3 times 2 over 2
c A LaTex expression showing 4 times 3 times 2 over 4 times 3 times 2 times 1
d A LaTex expression showing 3 times 2 over 2
e A LaTex expression showing 4 times 3 times 2 over 2 times 3 times 2