Duplications

Dupligrams

ANAGRAMS

WITH DUPLICATE LETTERS

Click & Drag Letters

Sometimes in Scrabble, we pick a horrible set of letters with so many duplicates we cannot possibly make a word. If we wanted to look at all the arrangements of such a word, how many ways could we distinguishably arrange its letters?

QUESTION: How many ways can you arrange all the letters in your name?
What if some letters in your name repeat, as in GEORGE, REBECCA, ANAMARIA, DANNIELLE? ASSIGNMENT: SET 1

a. Complete each row in the table.

Count the letters in the name in the WORD column.
In the n = LETTERS column, enter the number of letters in the name.
In the n! = PERMS column, enter the number of permutations of n letters
as if all the letters were different.
The DUPES column displays the duplicate letters.
The REPEATS column displays how many times duplicate letters repeat.
In the n! / j! / k! / r! column, enter the number of distinguishable permutations.

b. How many distinguishable ways can you arrange all the letters in your name?

Enter your first and last names in the WORD column. Press the ENTER key.
Do not use spaces. Use only letters.
In the LETTERS column, enter the number of letters in your name.
In the PERMS column, enter the number of permutations of n letters if all were different.
In the last column, enter the number of distinguishable permutations of all the letters in your name.

Assume that some n objects are NOT different.
There may be more than one object repeated.
Distinguishable order of the n objects is counted.

ASSIGNMENT: SET 2

How many ways can you arrange the Aces?
Click on an Ace to change its color.
Now how many ways can you arrange the Aces?
Fill in the table below with your answers.

For each row in the table above,
make a list of all the distinguishable permutations of the Aces.