Question

In how many ways can the letters in the word PROPORTIONALITY be arranged so that the vowels and consonants still occupy the same place?

Answer 1

Let's try :
Consonants: 8 places, 6 different letters => 6!
Vowels: 7 places, 4 different letters => 4!

4!*6!=17280 ?
But I'm quite sure I'm wrong :D

Answer 2

well the answer is 2, 721, 600

Answer 3

but i don't know how to get it

Answer 4

^^ haha...

Answer 5

are we considering Y a vowel? lol

Answer 6

lol:) u were close

Answer 7

no i don't think so

Answer 8

Really ? It's not a vowel in english ??

Answer 9

its just a,e,i,o,u isn't it

Answer 10

ok, im counting 9 consonants, so that makes 9!, but there are 2 P's, 2 R's, and 2 T's, so the number of arrangements is:
\[\frac{9!}{2!2!2!} = 45360\]

Now looking at the vowels, there are 6 of them, which is 6!, but there are 3 O's, and 2 I's, so the number of arrangements is:
\[\frac{6!}{3!2!} = 60\]
45360*60 = 2721600 total combinations.

Answer 11

Thanks for the explanation (and the discovery of Y not beeing a vowel :D)

Answer 12

oh k thanks for the working:)

Answer 13

Hmm, this is a bit bogus for a question. The y is clearly acting as a vowel.

Answer 14

i never thought y was a vowel until i looked it up on wikipedia lol

Answer 15

ive always seen it as not a vowel, but sometimes you hear, "AEIOU and sometimes Y" lol

Answer 16

yeah since primary school we've only been taught a,e,i,o,u

Answer 17

That's why I keep thinking that english pronunciation is hard >.< Always changing...

Answer 18

which country are you from?

Answer 19

France (I know, we suck at foreign language ^^)

Answer 20

i don't know about that lol. france has good music:)

Answer 21

Maybe ^^ Wondering what kind of french music can come to your ears

Answer 22

Alors on danse:)

Answer 23

Ok. Didn't know french music could travel that much apart from Daft Punk.
Btw, I think Stromae ("alors on danse") is actually from Belgium

Answer 24

he is from belgium, do they speak french in belgium?

Answer 25

is daft punk french i didn't know that

Answer 26

Daft punk is french yep.
For Belgians it's a story by itself... 50% speak french 50% dutch. There's kind of a political crisis currently there.

Answer 27

i see lol. thats interesting to know:)