Question

in how many ways can LGBASALLOTE be arranged?

Answer 1

i just want to see a demo on combination :p

Answer 2

It can be arranged in 11! / 2! * 3! ways.

Answer 3

how?

Answer 4

Since L and A appear 3 and two times respectively, and it contains 11 letters.

Answer 5

11 unique letters?

Answer 6

so @Diyadiya can be rearranged in \[\frac{8!}{4!}\]

Answer 7

Let's see then. We have 11 letters total, with 2 A's and 3 L's. So the total ways or arranging the letters is \(11!\). Now we need to get rid of the ones that are repeats.

Because of the 2 A's, we divide by \(2!\) since there are \(2!\) ways of ordering the two A's. Likewise, we also divide by \(3!\) since there are \(3!\) orderings of the L's.
Thus the total is \[{11!\over2!3!}\]

Answer 8

Diyadiya could be arranged in \[8!\over2!2!2!2!\]ways since you have 4 letters that repeat twice.

Answer 9

so total no. of letters! over product of how many times a letter repated!

Answer 10

Yes. It's more appropriate to say, as KingGeorge already pointed out that Diyadiya can be arranged in 8!/2!2!2!2! ways rather than saying 8!/4!

Answer 11

@KingGeorge can be rearranged in \[\large \frac{10!}{3!2!}\]

Answer 12

I believe that's correct.

Answer 13

and @Spacemanifestation can be rearranged in \[\large \frac{18!}{2!3!2!2!2!}\]

Answer 14

i think i got it thanks :D

Answer 15

Thanks , Even i got to know to arrange myself =D

Answer 16

but woudnt one rearrangement be disqualified? i mean when the second diya comes before the first diya? @KingGeorge

Answer 17

But we can also switch only the d's. Or only the i's. Or maybe the d's and the y's. So there's \(2!2!2!2!=2^4\) ways we can switch things around like that.

Answer 18

lol i dont want to look through this detailed-ly...too detailed :P