Enter Word Find unique arrangements for

MISSISSIPPI

Calculate Number of Arrangements

Arrangements = M! N_{1} !N_{2} !...N_{M} !

where M = letters in the word

and each N_{i} = dup letter occurrences

Calculate M

M = letters in the word

M = 11

Determine Duplicate Letters:

M I S S I S S I P P I :

I occurs 4 times, so N_{1} = 4

M I S S I S S I P P I :

S occurs 4 times, so N_{2} = 4

M I S S I S S I P P I :

P occurs 2 times, so N_{3} = 2

Plug in Values for Arrangements:

Arrangements = M! N_{1} !N_{2} !N_{3} !

Arrangements = 11! 4!4!2!

Calculate 11!

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

11! = 39916800

Calculate 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 4!

4! = 4 x 3 x 2 x 1

4! = 24

Calculate 2!

2! = 2 x 1

2! = 2

Plug in values and simply

Arrangements = 39,916,800 (24)(24)(2)

Arrangements = 39,916,800 1,152

Final Answer

Arrangements = 34,650

How does the Letter Arrangements in a Word Calculator work?
Free Letter Arrangements in a Word Calculator - Given a word, this determines the number of unique arrangements of letters in the word. This calculator has 1 input.

What 1 formula is used for the Letter Arrangements in a Word Calculator?
Arrangements = M!/N

_{1} !N

_{2} !...N

_{M} !

For more math formulas, check out our

Formula Dossier
What 3 concepts are covered in the Letter Arrangements in a Word Calculator?
factorial The product of an integer and all the integers below it letter arrangements in a word permutation a way in which a set or number of things can be ordered or arranged._{n} P_{r} = n!/(n - r)!

Example calculations for the Letter Arrangements in a Word Calculator
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