###### Asked in Math and Arithmetic

Math and Arithmetic

# Find the number of distinguishable permutations of the letters in the word calculator?

## Answer

###### Wiki User

###### June 01, 2009 2:58PM

Total permutations 10! ie factorial 10 = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 = 3628800. The 2 "c"s are interchangeable which halves this figure to 1814400, similarly the "a"s and "l"s are interchangeable which reduces by half twice more, ie to 907200 and then to 453600.

## Related Questions

###### Asked in Algebra, Probability

### How do you calculate distinguishable permutations?

The number of permutations of n distinct objects is n! = 1*2*3*
... *n.
If a set contains n objects, but k of them are identical
(non-distinguishable), then the number of distinct permutations is
n!/k!.
If the n objects contains j of them of one type, k of another,
then there are n!/(j!*k!).
The above pattern can be extended. For example, to calculate the
number of distinct permutations of the letters of "statistics":
Total number of letters: 10
Number of s: 3
Number of t: 3
Number of i: 2
So the answer is 10!/(3!*3!*2!) = 50400

###### Asked in Math and Arithmetic, Algebra, Probability

### Find the number of distinguishable permutations of the letters in the word Cincinnati?

There are ten letters in the word. The total number of possible
permutations is
(10) x (9) x (8) x (7) x (6) x (5) x (4) x (3) x (2) =
3,628,800
But the two 'c's can be arranged in either of 2 ways with no
distinguishable change.
Also, the three 'i's can be arranged in any of (3 x 2) = 6 ways
with no distinguishable change.
And the three 't's can be arranged in any of (3 x 2) = 6 ways
with no distinguishable change.
So the total number of possible permutations can be divided by
(2 x 6 x 6) = 72, the number of
times each distinguishable permutation occurs with different and
indisnguishable arrangements
of 'c', 'i', and 't'.
We're left with
(10) x (9) x (8) x (7) x (...) x (5) x (...) x (...) x (2) =
(3,628,800/72) = 50,400 distinguishable
arrangements.

###### Asked in Math and Arithmetic, Algebra, Gallipoli Campaign

### Find the number of distinguishable permutations of the letters in the word hippopotamus?

First of all, find the total number of not-necessarily
distinguishable permutations. There are 12 letters in hippopotamus,
so use 12! (12 factorial), which is equal to 12 x 11x 10 x9 x8 x7
x6 x5 x4 x3 x2 x1. 12! = 479001600.
Then count the of each letter and calculate how many
permutations of each letter can be made. For example, here is 1 h,
so there is 1 permutation of 1 h.
H 1
I 1
P 6
0 2
T 1
A 1
M 1
U 1
S 1
Multiply these numbers together. 1 x1 x6 x2 x1 x1 x1 x1 x1 =
12
Divide 12! by this number. 479001600 / 12 = 39,916,800
Distinguishable Permutations.

###### Asked in Probability

### How many ways can the letters in prealgebra can arranged?

The number of permutations of the letters in PREALGEBRA is the
same as the number of permutations of 10 things taken 10 at a time,
which is 3,628,800. However, since the letters R, E, and A, are
repeated, R=2, E=2, A=2, you must divide that by 2, and 2, and 2
(for a product of 8) to determine the number of distinct
permutations, which is 453,600.

###### Asked in Algebra, Geometry, Probability

### How many ways are there to arrange the letters in the word ADDRESS if the two Ds must be together?

The permutations of the letters ADDRESS if the two D's must be
together is the same as the permutations of the letters ADRESS,
which is 6 factorial, or 720, divided by 2, to compensate for the
two S's, which means that the number of distinct permutations of
the letters ADDRESS, where the two DD's must be together is
360.