Respuesta :

jamiechen79

Answer:

5040

Step-by-step explanation:

This problem is about indistinguishable permutation. We have indistinguishable objects, in this case, these are the letter of the word ELLIPSES. The permutations for the word ELLIPSES is the same when you swap the places of the Ls. We need to not count them to avoid double counting.

We first count how many letters we have on the word, and then count the repeating letters.

ELLIPSES has 8 letters, 2 Es, 2Ls, and 2S.

The formula for indistinguishable permutation is

where n is the total number of objects and  are the number of indistinguishable objects.

We have 2Es, 2Ls, and 2S; the formula then becomes:

Simplifying gives us

There are 5,040 distinguishable permutations of the word ELLIPSES.

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The total 5040 distinguishable permutations are possible with all the letters of the word ELLIPSES.

The given word is ELLIPSES.

It is required to find total distinguishable permutations that are possible with the above word.

What is permutation?

A permutation can be defined as the number of ways a set can be arranged.

Permutation formula as below:

[tex]P=\frac{n!}{p!q!r!...}[/tex]

Where n = Total number of objects.

     p,q,r...= the number of indistinguishable objects.

Here total number of letters in the word n = 8

and ELLIPSES have 2Es, 2Ls, and 2S; the formula then becomes:

[tex]=\frac{8!}{2!2!2!}[/tex]

[tex]=\frac{8*7*6*5*4*3*2*1}{2*1*2*1*2*1}[/tex]

[tex]=5040[/tex]

Thus, the total 5040 distinguishable permutations are possible with all the letters of the word ELLIPSES.

Learn more about permutation here:

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