Re: Combinatorial Analysis
- From: "almeidabatista@xxxxxxx" <almeidabatista@xxxxxxxxx>
- Date: Tue, 13 Nov 2007 05:47:07 -0800
On 13 nov, 09:00, "almeidabati...@xxxxxxx" <almeidabati...@xxxxxxxxx>
wrote:
Hi all! I'm stuck with this problems, can you give me any hints?
'What is the probability that a random arrangement of the letters in
MATHEMATICS has no consecutive vowels?'
Thanks in advance.
Just for the record, managed to solve it as follows, after reading the
textbook throughly:
I) Consider V and C as any vowel/consonant from the word MATHEMATICS.
II) Arrange all Vs and the necessary number of Cs so that you
guarantee that no Vs will be subsequent:
V C V C V C V
III) The remaining 4 Cs can be distributed in 5 places:
- to the left of 1st V
- btw. 1st and 2nd Vs
- btw. 2nd and 3rd Vs
- btw. 3rd and 4th Vs
- to the right of 4th V
This can be solved using the 'formula' for distributing r balls into n
spaces, with any number of balls per space, which is C(n - 1 + r,r) =
C(5 - 1 + 4, 4).
IV) Substitute the actual letters of the words into the Cs and Vs,
using permutation with repetition.
V) Use the Rule of Product
ANSWER: = [C(5 - 1 + 4,4) * (4!/2!) * (7!/2!2!)]/(11!/2!2!2!)
.
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