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Probability Counting - Duplicate Orders in 4 Cards, 2 Repeats - to Factorial Equation (Level 1)

This math topic focuses on calculating the different ways to arrange multiple cards where some cards are duplicates. Specifically, the problems require arranging four cards (some repeated), and determining the number of valid sequences using factorial notation. This involves principles of permutation, particularly permutations of multiset, which traditionally uses factorial calculations to solve problems involving n objects where certain objects are indistinguishable due to being repeats. These exercises cater to Introductory Probability and Statistics, specifically within the context of Binomial Notation.

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

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Duplicate Orders in 4 Cards, 2 Repeats - to Factorial Equation

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

How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.

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Probability Counting - Duplicate Orders in 4 Cards, 2 Repeats - to Factorial Equation Worksheet

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Math worksheet on 'Probability Counting - Duplicate Orders in 4 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
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 2! times 3!
b A LaTex expression showing 2! times 4!
c A LaTex expression showing 1 over 2! times 2!
d A LaTex expression showing 4! times 2!
e A LaTex expression showing 2! times 2!
f A LaTex expression showing 2! over 2! times 2!
2
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 4! times 2!
b A LaTex expression showing 2! times 2!
c A LaTex expression showing 2! times 4!
d A LaTex expression showing 3! times 2!
e A LaTex expression showing 2! over 2! times 2!
f A LaTex expression showing 1 over 2! times 2!
3
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 1 over 2! times 2!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 3! times 2!
d A LaTex expression showing 4! times 2!
e A LaTex expression showing 2! over 2! times 2!
f A LaTex expression showing 2! times 2!
4
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 4! times 2!
b A LaTex expression showing 1 over 2! times 2!
c A LaTex expression showing 2! over 2! times 2!
d A LaTex expression showing 2! times 4!
e A LaTex expression showing 2! times 3!
f A LaTex expression showing 2! times 2!
5
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 2! times 4!
b A LaTex expression showing 3! times 2!
c A LaTex expression showing 2! times 3!
d A LaTex expression showing 2! over 2! times 2!
e A LaTex expression showing 2! times 2!
f A LaTex expression showing 1 over 2! times 2!
6
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 2! times 3!
b A LaTex expression showing 2! over 2! times 2!
c A LaTex expression showing 2! times 2!
d A LaTex expression showing 3! times 2!
e A LaTex expression showing 4! times 2!
f A LaTex expression showing 1 over 2! times 2!
7
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a factorial.
An svg image showing a math problem
a A LaTex expression showing 2! times 3!
b A LaTex expression showing 2! over 2! times 2!
c A LaTex expression showing 2! times 2!
d A LaTex expression showing 3! times 2!
e A LaTex expression showing 2! times 4!
f A LaTex expression showing 1 over 2! times 2!