Find unique arrangements for
MISSISSIPPI
Calculate Number of Arrangements
| Arrangements = | M! |
| N1!N2!...NM! |
where M = letters in the word
and each Ni = dup letter occurrences
Calculate M
M = letters in the word
M = 11
Determine Duplicate Letters:
MISSISSIPPI:
I occurs 4 times, so N1 = 4
MISSISSIPPI:
S occurs 4 times, so N2 = 4
MISSISSIPPI:
P occurs 2 times, so N3 = 2
Plug in Values for Arrangements:
| Arrangements = | M! |
| N1!N2!N3! |
| 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
What is the 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.
This calculator has 1 input.
What 1 formula is used for the Letter Arrangements in a Word Calculator?
Arrangements = M!/N1!N2!...NM!
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.
nPr = n!/(n - r)!
