Duplicate Orders in 3 Cards, 1 Repeat - to Factorial Equation (Level 1)

This math topic focuses on probability and factorial equations related to the arrangements of card sequences. It tests the ability to determine the number of valid arrangements of cards (given repeats and without) to remain in ascending order, using factorial notation. Questions may require learners to apply factorial calculations directly or solve for arrangements based on specific repeats and order conditions. The problems require understanding factorial concepts in a context of probability, crucial for grasping more complex topics in probability and statistics.

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

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Probability Counting - Duplicate Orders in 3 Cards, 1 Repeat - to Factorial Equation Worksheet

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Probability Counting - Duplicate Orders in 3 Cards, 1 Repeat - to Factorial Equation
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 2!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 1 over 2! times 1!
d A LaTex expression showing 2!
e A LaTex expression showing 4!
f A LaTex expression showing 2! over 2! times 1!
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!
b A LaTex expression showing 3!
c A LaTex expression showing 2!
d A LaTex expression showing 2! over 2! times 1!
e A LaTex expression showing 1 over 2! times 1!
f A LaTex expression showing 2! times 3!
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 1!
b A LaTex expression showing 3!
c A LaTex expression showing 4!
d A LaTex expression showing 2!
e A LaTex expression showing 2! times 2!
f A LaTex expression showing 2! over 2! times 1!
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!
b A LaTex expression showing 2! times 2!
c A LaTex expression showing 2! times 3!
d A LaTex expression showing 2! over 2! times 1!
e A LaTex expression showing 1 over 2! times 1!
f A LaTex expression showing 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 2!
b A LaTex expression showing 2!
c A LaTex expression showing 4!
d A LaTex expression showing 2! times 3!
e A LaTex expression showing 2! over 2! times 1!
f A LaTex expression showing 1 over 2! times 1!
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 2!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 1 over 2! times 1!
d A LaTex expression showing 4!
e A LaTex expression showing 2! over 2! times 1!
f A LaTex expression showing 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 1 over 2! times 1!
b A LaTex expression showing 2! over 2! times 1!
c A LaTex expression showing 2!
d A LaTex expression showing 4!
e A LaTex expression showing 3!
f A LaTex expression showing 2! times 2!
8
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 2!
c A LaTex expression showing 2! over 2! times 1!
d A LaTex expression showing 3!
e A LaTex expression showing 1 over 2! times 1!
f A LaTex expression showing 2!