Juliastcarenealynethidn
Answered

Makakuha ng detalyadong mga sagot sa iyong mga tanong gamit ang IDNStudy.com. Magtanong at makatanggap ng eksaktong sagot mula sa aming mga bihasang miyembro ng komunidad.

How many distinguishable permutations are possible with all the letters of the word ELLIPSES?

Sagot :

Rylai04idn

Answer:

5,040

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

[tex]\frac{n!}{n_{1}!n_{2}!...n_{k}! }[/tex]

where n is the total number of objects and [tex]n_{k}[/tex] are the number of indistinguishable objects.

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

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

Simplifying gives us

[tex]= \frac{8!}{2!2!2!}\\\\= \frac{8*7*6*5*4*3*2*1}{2*2*2}\\\\= 8*7*6*5*3\\\\= 5,040[/tex]

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

For more information about indistinguishable permutations, click here

https://brainly.ph/question/2487180

https://brainly.ph/question/2479274

https://brainly.ph/question/2470260

https://brainly.ph/question/2470259

Maraming salamat sa iyong pakikilahok. Huwag kalimutang bumalik at magtanong ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. Ang IDNStudy.com ang iyong mapagkakatiwalaang mapagkukunan ng mga sagot. Salamat at bumalik ka ulit.