Question

How many different arrangements can be made with the word DIVIDE?

Answer 1

564894564

Answer 2

Do they have to be real words?

Answer 3

nahh.. just arrangements with the given letters...

Answer 4

I would say 6! = 720

Answer 5

Do you have to use all 6?

Answer 6

Deox.. that seems right, but would you do anything different because of the double D's and I's

Answer 7

?

Answer 8

I would say 6! + 5! + 4! + 3! + 2! + 1 because you can have 1-6 long words.

Answer 9

The answer would be 4! since there are only 4 separate letters in the word.

Answer 10

k... i think thats right.. its 4 becuz there are 2 repeats in the 6 letter word, right?

Answer 11

You take the total number of letters factorial on top, \(6!\), and then any letters that repeat you put factorials on the bottom for how many of those letters there are. This one we have two Ds and two Is, so we do \(2!2!\) on the bottom. So we have the result \(\dfrac{6!}{2!2!}\)

Answer 12

Using this as a reference the answer would actually be
6! / (2!2!)
http://answers.yahoo.com/question/index?qid=20080924110152AAaooQO

Answer 13

I got 4!=24 is that right?

Answer 14

@carlo26 It isn't \(4!\), it's \(\dfrac{6!}{2!2!}\)

@ everyone else, please don't answer if you don't know the answer.

Answer 15

nbouscal's answer is correct

Answer 16

No, @PsychoTink is right, the things is that 6! gives you the total number of possibilities, then you divide by half (2!) to eliminate repeated D's and then by half again to remove repeated I's.

Answer 17

nbouscal, I'm not saying you're wrong, but we have been getting numerical values in class... i dont recall seeing answers like urs

Answer 18

Ok, what I did was I counted the letters.. There is 6, but there are 2 repeats.. Therefore there are basically 4 letters.. I then plugged 4! into the calculator, then I got 24.. is that correct?

Answer 19

You just have to simplify it. \(\dfrac{6!}{2!2!}\) is the same as \(\dfrac{6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot2\cdot1}\), you can cancel out to simplify it to \(6\cdot5\cdot3\cdot2\cdot1\), which is 180.

Answer 20

Or alternatively you can do 6!=720, 2!2!=4, 720/4=180

Answer 21

Ok.. So I shouldn't be worried about the repeats?

Answer 22

The repeats are how we got the 2!2! in the denominator, did you read my post?

Answer 23

yea... it's just a bit confusing buddy.. I think I got it now tho :D thx for the help

Answer 24

so then the word ABSCISSA would go like this..... 8! / 2! ?

Answer 25

The link I posted helps explain it as well if you're still confused, but it's basically total letters on top, on bottom you do any repeats so for d and i each repeats twice so that's 2 and 2.

Answer 26

No, abiscissa would be /3! because there are 3 s's

Answer 27

ABSCISSA has 8 letters total, so the top is 8!, but the S repeats 3 times and the A repeats 2 times, so the bottom is 3!2!

Answer 28

actually /3!2! because there are 2a's as well

Answer 29

ok.. and i solve that by just plugging the numbers in, right

Answer 30

You can expand it or plug it into a calculator. Most calculators have the ! function.

Answer 31

yea mine does, thanks so much guys, I appreciate the help!