Duplicate Orders in 5 Letters, 2 Repeats - to Factorial Equation (Level 1)

This math topic focuses on calculating probabilities of different permutations of words formed using specific sets of letters with repeated characters. The problems require expressing the solutions using factorial notation. Specifically, students practice solving the number of ways to arrange letters in words like "MAMMA," "PAPPA," "DADDA," "LEVEL," and "VIVID," applying knowledge of factorials and permutation formulas where repetitions are present. This involves understanding and applying formulas from the probability and statistics segment, particularly binomial notation.

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

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Probability Counting - Duplicate Orders in 5 Letters, 2 Repeats - to Factorial Equation Worksheet

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Probability Counting - Duplicate Orders in 5 Letters, 2 Repeats - to Factorial Equation
1
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'LEVEL'? Show as a factorial.
a A LaTex expression showing 2! times 2!
b A LaTex expression showing 1 over 2! times 2!
c A LaTex expression showing 2! times 4!
d A LaTex expression showing 4! times 2!
e A LaTex expression showing 2! over 2! times 2!
f A LaTex expression showing 2! times 3!
2
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'PAPPA'? Show as a factorial.
a A LaTex expression showing 4! times 3!
b A LaTex expression showing 2! over 2! times 3!
c A LaTex expression showing 1 over 2! times 3!
d A LaTex expression showing 2! times 5!
e A LaTex expression showing 2! times 3!
f A LaTex expression showing 3! times 3!
3
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'DADDA'? Show as a factorial.
a A LaTex expression showing 2! over 3! times 2!
b A LaTex expression showing 5! times 2!
c A LaTex expression showing 1 over 3! times 2!
d A LaTex expression showing 3! times 3!
e A LaTex expression showing 3! times 4!
f A LaTex expression showing 3! times 2!
4
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'MAMMA'? Show as a factorial.
a A LaTex expression showing 2! times 3!
b A LaTex expression showing 2! times 4!
c A LaTex expression showing 4! times 3!
d A LaTex expression showing 1 over 2! times 3!
e A LaTex expression showing 2! times 5!
f A LaTex expression showing 3! times 3!
5
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'VIVID'? Show as a factorial.
a A LaTex expression showing 2! times 4!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 3! times 2!
d A LaTex expression showing 1 over 2! times 2!
e A LaTex expression showing 2! over 2! times 2!
f A LaTex expression showing 2! times 2!
6
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'PAPPA'? Show as a factorial.
a A LaTex expression showing 1 over 3! times 2!
b A LaTex expression showing 2! over 3! times 2!
c A LaTex expression showing 3! times 2!
d A LaTex expression showing 3! times 3!
e A LaTex expression showing 4! times 2!
f A LaTex expression showing 3! times 4!
7
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'MAMMA'? Show as a factorial.
a A LaTex expression showing 3! times 4!
b A LaTex expression showing 5! times 2!
c A LaTex expression showing 4! times 2!
d A LaTex expression showing 1 over 3! times 2!
e A LaTex expression showing 2! over 3! times 2!
f A LaTex expression showing 3! times 2!
8
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'DADDA'? Show as a factorial.
a A LaTex expression showing 1 over 2! times 3!
b A LaTex expression showing 2! times 5!
c A LaTex expression showing 2! times 3!
d A LaTex expression showing 2! times 4!
e A LaTex expression showing 2! over 2! times 3!
f A LaTex expression showing 4! times 3!