!!help the letters of the word tuesday are arranged in a row what is the probability (1 Viewer)

bubb · Sep 7, 2015

!!help the letters of the word tuesday are arranged in a row what is the probability the vowels are together and the letter "T" occupies the first place?

InteGrand · Sep 7, 2015

Re: !!help the letters of the word tuesday are arranged in a row what is the probabil

bubb said:
!!help the letters of the word tuesday are arranged in a row what is the probability the vowels are together and the letter "t" occupies the first place?

$We need configurations like this:$

$\textit{T[UEA]SDY}$

$\noindent where we have used brackets to group the vowels together to help visualise the vowels as one unit. The $T$ must be in the first position. With the remaining six letters (or \textbf{four} ``units'': 3 single letters and one ``group'' of vowels), we can arrange them in $4! \cdot 3!$ ways so that the vowels are together (as there are $4!$ ways to arrange the four units, and for each of these ways, there are $3!$ ways to arrange the vowels). The total number of ways to arrange the letters of \textit{TUESDAY} without restriction is just $7!$. Hence the required probability is $\boxed{\frac{4!\cdot 3!}{7!}=\frac{3!}{7\times 6 \times 5}=\frac{1}{35}}$.$

AztecWarrior · Sep 7, 2015

Re: !!help the letters of the word tuesday are arranged in a row what is the probabil

Above is right

PhysicsMaths · Sep 7, 2015

Re: !!help the letters of the word tuesday are arranged in a row what is the probabil

There are 3 vowels and T is fixed in the 1st spot

Group the three vowels together, and they can be arranged in 3! ways
T(U E A) S D Y

Also, consider them collectively as one letter, so the remaining letters can be arranged in 4! ways
So the total arrangements = 3!x4! = 144 ways

Also, total arrangements without restrictions = 7!
So probability = 3!x4!/7! = 1/35

!!help the letters of the word tuesday are arranged in a row what is the probability (1 Viewer)

bubb

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InteGrand

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AztecWarrior

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PhysicsMaths

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