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Probability Counting - Ways to Order 5 Cards, 2 Repeat - to Equation (Level 1)

This math topic focuses on solving probability problems related to ordering scenarios involving 5 cards, where some cards may be identical, thus introducing repetition in possible combinations. The skills practiced include calculating the number of distinct ways to order these cards, presented primarily through factorial and permutation concepts, key components in probability and statistics. Specifically, the material introduces the binomial notation and challenges students to express their answers as multiplication expressions, to better grasp the fundamental counting principles that govern permutation and combination calculations in probability theory.

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

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Ways to Order 5 Cards, 2 Repeat - to Equation

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


How many distinct ways can these cards be ordered? Show as a multiplication.

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Probability Counting - Ways to Order 5 Cards, 2 Repeat - to Equation Worksheet

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