Find unique arrangements for
CALCULUS
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 = 8
Determine Duplicate Letters:
CALCULUS:
C occurs 2 times, so N1 = 2
CALCULUS:
L occurs 2 times, so N2 = 2
CALCULUS:
U occurs 2 times, so N3 = 2
Plug in Values for Arrangements:
| Arrangements = | M! |
| N1!N2!N3! |
| Arrangements = | 8! |
| 2!2!2! |
Calculate 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40320
Calculate 2!
2! = 2 x 1
2! = 2
Calculate 2!
2! = 2 x 1
2! = 2
Calculate 2!
2! = 2 x 1
2! = 2
Plug in values and simply
| Arrangements = | 40,320 |
| (2)(2)(2) |
| Arrangements = | 40,320 |
| 8 |
Final Answer
Arrangements = 5,040
What is the Answer?
Arrangements = 5,040
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)!
