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You pick a word at random from the set of all words of length six of letters of the alphabet with no repeated letters. What is the probability that the word begins and ends with a vowel

Sagot :

Answer: [tex]\dfrac{2}{65}[/tex]

Step-by-step explanation:

Given

There is a six letter word with no repeated letters

Number of ways of arranging 6 letters out of 26 letters is [tex]^{26}P_6[/tex]

For the 6 letter word with vowels in the beginning and the end can be formed by selecting 2 vowels out of 5 available.

First place has 5 choices to fill and the last place left with 4 choices to fill

Remaining 4 places can be filled by [tex]^{24}P_4[/tex] ways

So, the required probability is given by

[tex]\Rightarrow \dfrac{5\times ^{24}P_4\times 4}{^{26}P_6}=\dfrac{2}{65}[/tex]

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