little help plz (1 Viewer)

[Pace_T]

hey all
i dun understand this question:
Find the number of ways in which the letters of the word EXTENSION can be arranged in a straight line so that no two vowels are next to each other.
i got the answer but i dont know how they got that
its from the 2001 cssa paper
thx

 

[klaw]

it's a permutations and combinations question... I forgot all about that topic

 

[acmilan]

There are 9 letters, 5 consonants and 4 vowels, the only form it can be written in so that there are no vowels together is:

CVCVCVCVC

So you just consider the C's and V's separately, C's can be arranged 5!/2! ways (since there are 2 N's you divide by 2!) and V's 4!/2! ways (since there are 2 E's you divide by 2!). So together is (5!x4!)/(2!x2!) = 60x12 = 720

Is that right?

 

[Pace_T]

yea thats right
but i dun understand
what about
CCVCVCVCV
and
VCVCVCVCC
(that is, the vowels shift to the left and the right)??
woah i am totally confused here
thx

 

[acmilan]

hmmm i guess what they meant is arrange it so that they alternate?

 

[Trev]

My teacher went through this question with us, saying that it's a mistake how they allocated 2 marks or something for a question that appears so early in the paper and is more difficult if you do it properly. Something like that... lol.

 

[insert-username]

I think you need to multiply 720 by 3 - you have 720 ways to arrange it CVCVCVCVC, another 720 for CCVCVCVCV, and another 720 for VCVCVCVCC. So 720x3 = 2160 ways. I think that's right...


I_F

 

[Pace_T]

hmm ye thats what i was thinking
thx eerbody