Permutations with Repetition — Basics

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7049 | Total Attempts: 9,519,298
| Questions: 10
Please wait...
Question 1 / 10
0 %
0/100
Score 0/100
1) Find the number of distinct permutations of the letters in "LEVEL".

Explanation

“LEVEL” has 5 letters with L repeated 2 times and E repeated 2 times: 5!/(2!·2!) = 120/4 = 30.

Submit
Please wait...
About This Quiz
Permutations With Repetition Basics - Quiz

Sometimes choices repeat, and that changes the math! In this quiz, you’ll explore how to calculate permutations when repetition is allowed. Try this quiz to understand how patterns grow when repeats are possible.

2)
We’ll put your name on your report, certificate, and leaderboard.
2) Find the number of distinct permutations of the letters in “BALLOON”.

Explanation

“BALLOON” has 7 letters with L repeated 2 times and O repeated 2 times: 7!/(2!·2!) = 5040/4 = 1260.

Submit
3) How many 5-digit numbers can be formed using the digits 1,1,1,2,3?

Explanation

Five symbols with 1 repeated thrice: 5!/3! = 120/6 = 20.

Submit
4) Find the number of distinct arrangements of the letters in “SUCCESS”.

Explanation

“SUCCESS” has 7 letters with S repeated 3 times and C repeated 2 times: 7!/(3!·2!) = 5040/12 = 420.

Submit
5) Find the number of distinct arrangements of the letters in “TATTOO”.

Explanation

“TATTOO” has 6 letters with T repeated 3 times and O repeated 2 times: 6!/(3!·2!) = 720/12 = 60.

Submit
6) Find the number of arrangements of the letters in “MISSISSIPPI”.

Explanation

“MISSISSIPPI” has 11 letters: I=4, S=4, P=2 → 11!/(4!·4!·2!) = 39,916,800 / 1,152 = 34,650.

Submit
7) Find the number of arrangements of the letters in “MOON”.

Explanation

“MOON” has 4 letters with O repeated twice: 4!/2! = 24/2 = 12.

Submit
8) Find the number of 6-letter arrangements possible from “BANANA”.

Explanation

“BANANA” has 6 letters with A=3 and N=2: 6!/(3!·2!) = 720/12 = 60.

Submit
9) Find the number of arrangements of the digits 2,2,3,3,3.

Explanation

Five digits with 2 repeated twice and 3 repeated thrice: 5!/(2!·3!) = 120/12 = 10.

Submit
10) Find the number of arrangements of the letters in “BOOKKEEPER”.

Explanation

“BOOKKEEPER” has 10 letters with O=2, K=2, E=3: 10!/(2!·2!·3!) = 3,628,800 / 24 = 151,200.

Submit
View My Results

Quiz Review Timeline (Updated): Oct 13, 2025 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Oct 13, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 07, 2025
    Quiz Created by
    Thames
Cancel
  • All
    All (10)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Find the number of distinct permutations of the letters in "LEVEL".
Find the number of distinct permutations of the letters in...
How many 5-digit numbers can be formed using the digits 1,1,1,2,3?
Find the number of distinct arrangements of the letters in...
Find the number of distinct arrangements of the letters in...
Find the number of arrangements of the letters in “MISSISSIPPI”.
Find the number of arrangements of the letters in “MOON”.
Find the number of 6-letter arrangements possible from “BANANA”.
Find the number of arrangements of the digits 2,2,3,3,3.
Find the number of arrangements of the letters in “BOOKKEEPER”.
Alert!

Back to Top Back to top
Advertisement