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

This math topic focuses on calculating the number of ways to arrange letters with duplicates, using factorial notation. It explores permutations in scenarios where certain letters in a three-letter word repeat. Each problem provides a word with either one or two identical letters and asks for the arrangement possibilities shown as different factorial expressions or products of factorials. These exercises are designed to help understand the fundamentals of factorials in probability and permutations, specifically when dealing with duplicate elements.

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

more
View

Probability Counting - Duplicate Orders in 3 Letters, 1 Repeat - to Factorial Equation Worksheet

Mobius Math Academy logo
Probability Counting - Duplicate Orders in 3 Letters, 1 Repeat - to Factorial Equation
1
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'NON'? Show as a factorial.
a A LaTex expression showing 2! times 2!
b A LaTex expression showing 2! over 2! times 1!
c A LaTex expression showing 4!
d A LaTex expression showing 2! times 3!
e A LaTex expression showing 1 over 2! times 1!
f A LaTex expression showing 2!
2
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'APP'? Show as a factorial.
a A LaTex expression showing 3!
b A LaTex expression showing 2! over 2! times 1!
c A LaTex expression showing 4!
d A LaTex expression showing 2!
e A LaTex expression showing 2! times 3!
f A LaTex expression showing 1 over 2! times 1!
3
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'BOB'? Show as a factorial.
a A LaTex expression showing 2!
b A LaTex expression showing 3!
c A LaTex expression showing 4!
d A LaTex expression showing 1 over 2! times 1!
e A LaTex expression showing 2! over 2! times 1!
f A LaTex expression showing 2! times 3!
4
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'ALL'? Show as a factorial.
a A LaTex expression showing 2! times 2!
b A LaTex expression showing 2! over 2! times 1!
c A LaTex expression showing 4!
d A LaTex expression showing 2!
e A LaTex expression showing 1 over 2! times 1!
f A LaTex expression showing 2! times 3!
5
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'POP'? Show as a factorial.
a A LaTex expression showing 1 over 2! times 1!
b A LaTex expression showing 3!
c A LaTex expression showing 2! times 3!
d A LaTex expression showing 2!
e A LaTex expression showing 2! over 2! times 1!
f A LaTex expression showing 4!
6
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'OFF'? Show as a factorial.
a A LaTex expression showing 3!
b A LaTex expression showing 2! times 3!
c A LaTex expression showing 2! over 2! times 1!
d A LaTex expression showing 4!
e A LaTex expression showing 2!
f A LaTex expression showing 1 over 2! times 1!
7
An svg image showing a math problem
How many ways can these letter tiles be ordered to spell 'INN'? Show as a factorial.
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! times 3!
d A LaTex expression showing 2! times 2!
e A LaTex expression showing 3!
f A LaTex expression showing 2!