Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.