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Probability Counting - Duplicate Orders in 5 Cards, 1 Repeat - to Factorial Equation (Level 1)

This math topic focuses on the calculation of probabilities involving factorials, specifically through exercises about arranging a set of cards, some of which are duplicates, in orders from smallest to largest. It challenges students to understand and apply factorial concepts to find the number of valid arrangements of cards, considering repetitions. Each question presents different configurations of cards and asks for the count of valid sequences that preserve a specified order, which is to be expressed as a factorial equation. The topic is part of a broader study on probability and statistics involving factorials.

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

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Duplicate Orders in 5 Cards, 1 Repeat - 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.

8910JJ

Probability Counting - Duplicate Orders in 5 Cards, 1 Repeat - to Factorial Equation Worksheet

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Math worksheet on 'Probability Counting - Duplicate Orders in 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
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 3!
b A LaTex expression showing 3! times 3!
c A LaTex expression showing 4!
d A LaTex expression showing 1 over 3! times 1!
e A LaTex expression showing 2! over 3! times 1!
f A LaTex expression showing 3! 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 3! times 2!
b A LaTex expression showing 5!
c A LaTex expression showing 3!
d A LaTex expression showing 1 over 3! times 1!
e A LaTex expression showing 2! over 3! times 1!
f A LaTex expression showing 4!
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 3! times 2!
b A LaTex expression showing 3! times 3!
c A LaTex expression showing 2! over 3! times 1!
d A LaTex expression showing 5!
e A LaTex expression showing 4!
f A LaTex expression showing 3!
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 1 over 3! times 1!
b A LaTex expression showing 3! times 3!
c A LaTex expression showing 5!
d A LaTex expression showing 3! times 2!
e A LaTex expression showing 3!
f A LaTex expression showing 2! over 3! times 1!
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 2!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 2! over 2! times 1!
d A LaTex expression showing 1 over 2! times 1!
e A LaTex expression showing 3!
f A LaTex expression showing 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 1 over 2! times 1!
b A LaTex expression showing 2! over 2! times 1!
c A LaTex expression showing 2! times 3!
d A LaTex expression showing 2!
e A LaTex expression showing 2! times 2!
f A LaTex expression showing 3!
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 1 over 3! times 1!
b A LaTex expression showing 5!
c A LaTex expression showing 2! over 3! times 1!
d A LaTex expression showing 3! times 2!
e A LaTex expression showing 3!
f A LaTex expression showing 3! times 3!