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

This math topic focuses on the probability and statistics skills involving calculations with factorials, specifically calculating possible arrangements of cards including scenarios with repeated elements. The problems ask students to determine the number of ways cards can be arranged in increasing order when some cards may be identical, illustrated with expressions related to permutations and combinations. Each problem offers multiple choices represented by mathematical expressions and calculations. These exercises serve as an introduction to understanding and manipulating factorials in probabilistic contexts.

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 Equation Worksheet

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Probability Counting - Duplicate Orders in 3 Cards, 1 Repeat - to Equation
1
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 2 over 2 times 1
b A LaTex expression showing 2
c A LaTex expression showing 2 times 3 times 2
d A LaTex expression showing 3 times 2
e A LaTex expression showing 4 times 3 times 2
f A LaTex expression showing 1 over 2 times 1
2
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 1 over 2 times 1
b A LaTex expression showing 2 times 3 times 2
c A LaTex expression showing 2 over 2 times 1
d A LaTex expression showing 2
e A LaTex expression showing 3 times 2
f A LaTex expression showing 4 times 3 times 2
3
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 3 times 2
b A LaTex expression showing 2 over 2 times 1
c A LaTex expression showing 2
d A LaTex expression showing 1 over 2 times 1
e A LaTex expression showing 2 times 2
f A LaTex expression showing 4 times 3 times 2
4
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
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 2 times 3 times 2
d A LaTex expression showing 3 times 2
e A LaTex expression showing 1 over 2 times 1
f A LaTex expression showing 4 times 3 times 2
5
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 1 over 2 times 1
b A LaTex expression showing 2
c A LaTex expression showing 3 times 2
d A LaTex expression showing 2 times 2
e A LaTex expression showing 4 times 3 times 2
f A LaTex expression showing 2 over 2 times 1
6
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 2 over 2 times 1
b A LaTex expression showing 1 over 2 times 1
c A LaTex expression showing 2
d A LaTex expression showing 4 times 3 times 2
e A LaTex expression showing 2 times 2
f A LaTex expression showing 2 times 3 times 2
7
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 1 over 2 times 1
b A LaTex expression showing 3 times 2
c A LaTex expression showing 2 over 2 times 1
d A LaTex expression showing 2
e A LaTex expression showing 2 times 3 times 2
f A LaTex expression showing 4 times 3 times 2
8
How many ways can these cards be arranged to still be arranged smallest to largest? Show as a multiplication.
An svg image showing a math problem
a A LaTex expression showing 3 times 2
b A LaTex expression showing 4 times 3 times 2
c A LaTex expression showing 2 over 2 times 1
d A LaTex expression showing 2 times 3 times 2
e A LaTex expression showing 1 over 2 times 1
f A LaTex expression showing 2