Ways to Order 5 Cards, 1 Repeat - to Equation (Level 1)

This math topic focuses on calculating permutations, particularly how to order 5 cards with one repeated card, using factorial concepts. It enhances skills in setting up factorial equations to determine the number of distinct ways to arrange a given set of items where order matters and when there are repetitions. The problems present mathematical expression options and students must select the correct formulation to represent the permutations possible under specified conditions. Overall, it aims to provide practice in probability calculations using permutation principles, part of a broader unit on probability and statistics.

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

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Probability Counting - Ways to Order 5 Cards, 1 Repeat - to Equation Worksheet

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Probability Counting - Ways to Order 5 Cards, 1 Repeat - to Equation
1
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 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
b A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
c A LaTex expression showing 7 times 6 times 5 times 4 times 3 times 2 over 2 times 3 times 2
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 5 times 4 times 3 times 2 over 3 times 2 times 2
b A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
d A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
e A LaTex expression showing 3 times 2 over 3 times 2
f A LaTex expression showing 4 times 3 times 2 over 3 times 2
3
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 3 times 2
b A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2 times 3 times 2
c A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 3 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
e A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
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 7 times 6 times 5 times 4 times 3 times 2 over 3 times 2 times 2
b A LaTex expression showing 7 times 6 times 5 times 4 times 3 times 2 over 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
e A LaTex expression showing 5 times 4 times 3 times 2 over 2
f A LaTex expression showing 5 times 4 times 3 times 2 over 4 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 5 times 4 times 3 times 2 over 3 times 2 times 3 times 2
b A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
c A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 4 times 3 times 2
e A LaTex expression showing 3 times 2 over 3 times 2
f A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2
6
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 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
b A LaTex expression showing 3 times 2 over 2
c A LaTex expression showing 5 times 4 times 3 times 2 over 2
d A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 2 times 2
e A LaTex expression showing 5 times 4 times 3 times 2 over 2 times 2
f A LaTex expression showing 5 times 4 times 3 times 2 over 2 times 3 times 2
7
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 5 times 4 times 3 times 2 over 4 times 3 times 2
b A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
c A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 3 times 2 times 2
d A LaTex expression showing 7 times 6 times 5 times 4 times 3 times 2 over 3 times 2 times 2
e A LaTex expression showing 5 times 4 times 3 times 2 over 2
f A LaTex expression showing 3 times 2 over 2
8
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 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2
b A LaTex expression showing 5 times 4 times 3 times 2 over 5 times 4 times 3 times 2 times 1
c A LaTex expression showing 6 times 5 times 4 times 3 times 2 over 3 times 2 times 3 times 2
d A LaTex expression showing 5 times 4 times 3 times 2 over 4 times 3 times 2
e A LaTex expression showing 4 times 3 times 2 over 3 times 2
f A LaTex expression showing 5 times 4 times 3 times 2 over 3 times 2