Ways to Order 4 Letters, 2 Repeats - to Factorial Equation (Level 1)

This math topic focuses on calculating the number of distinct ways to order a set of four letter tiles, containing some repeated letters, using factorial equations. It leverages principles of permutations where repetition occurs, applying factorial notation to solve the problems. This involves the use of formulas such as \( \frac{n!}{p! \times q!} \), where \( n \) is the total number of items to arrange, and \( p \) and \( q \) are the numbers of repeated items. This topic is an introductory part of learning about probability, statistics, and binomial notation.

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

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Probability Counting - Ways to Order 4 Letters, 2 Repeats - to Factorial Equation Worksheet

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Probability Counting - Ways to Order 4 Letters, 2 Repeats - to Factorial Equation
1
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 4! times 0!
b A LaTex expression showing 4! over 2! times 2!
c A LaTex expression showing 4! over 2! times 4!
d A LaTex expression showing 4! over 2! times 3!
e A LaTex expression showing 4! over 4! times 2!
f A LaTex expression showing 3! over 2! times 2!
2
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 3! times 2!
b A LaTex expression showing 4! over 2! times 4!
c A LaTex expression showing 4! over 4! times 2!
d A LaTex expression showing 4! over 4! times 0!
e A LaTex expression showing 4! over 2! times 2!
3
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 2! times 2!
b A LaTex expression showing 5! over 2! times 2!
c A LaTex expression showing 5! over 2! times 2! times 2!
d A LaTex expression showing 4! over 4! times 0!
e A LaTex expression showing 3! over 2! times 2!
f A LaTex expression showing 6! over 2! times 2!
4
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 2! times 2!
b A LaTex expression showing 3! over 2! times 2!
c A LaTex expression showing 4! over 2! times 4!
d A LaTex expression showing 4! over 4! times 0!
e A LaTex expression showing 4! over 4! times 2!
5
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 3! over 2! times 2!
b A LaTex expression showing 6! over 2! times 2!
c A LaTex expression showing 4! over 4! times 0!
d A LaTex expression showing 4! over 2! times 2!
e A LaTex expression showing 4! over 3! times 2!
f A LaTex expression showing 5! over 2! times 2! times 2!
6
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 2! times 3!
b A LaTex expression showing 4! over 2! times 2!
c A LaTex expression showing 4! over 2! times 4!
d A LaTex expression showing 4! over 4! times 0!
7
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 2! times 4!
b A LaTex expression showing 6! over 2! times 2!
c A LaTex expression showing 3! over 2! times 2!
d A LaTex expression showing 5! over 2! times 2!
e A LaTex expression showing 4! over 4! times 0!
f A LaTex expression showing 4! over 2! times 2!
8
An svg image showing a math problem
How many distinct ways can these letter tiles be ordered? Show as a factorial.
a A LaTex expression showing 4! over 2! times 2!
b A LaTex expression showing 5! over 2! times 2!
c A LaTex expression showing 4! over 4! times 0!
d A LaTex expression showing 3! over 2! times 2!
e A LaTex expression showing 4! over 3! times 2!
f A LaTex expression showing 4! over 2! times 3!