Problem

Selecting a Jury How many ways can a jury of 6 wo…

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Problem 45 Medium Difficulty

Hawaiian Words The Hawaiian alphabet consists of 7 consonants and 5 vowels. How many three-letter “words” are possible if there are never two consonants together and if a word must always end in a vowel?

Answer

350

Related Courses

Intro Stats / AP Statistics

Elementary Statistics a Step by Step Approach

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

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John D.

February 27, 2021

The video says the answer is 475. The answer listed under "answer" is 350. Which is it?

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Video Transcript

Okay, so there are seven continents and five balls in the Hawaiian alphabet. Now, how many three letter words can you form under these two conditions? Two continents are never together, and words always end in a bubble. Okay, so remember, we're only forming three letter words. So let's look at the possible structure off these words, right? So since the last letter always needs to be a vowel all right and two continents air never together. One possible structure would be a continent followed by your bowel and then another vowel. Another possibility would be it's a vowel at the end. First letters. Your bowel second letter would be a continent. Now there's a third possibility we could have ah, word with no continents at all. So that means valuable on the first, second and third positions. Right now, we're going to use the fundamental counting principle. Applied 23 events so fundamental counting rule or principle. So, in a sequence of three events in which the first one has que one possibilities, second event has K two possibilities third, Aventis Katie possibilities. Then the total number of possibilities for the sequence will be given by K one time skate, too. I'm skate three. So let's determine how maney possibilities for each of this word structure. So there are seven continents times There are five bubbles times five miles. All right, we're assuming weekend we can repeat, uh, bobbles. In this case, we can repeat the letters for the second structure here. It's gonna be There's five vowels time, seven continents, times five bubbles. The last possible structure would be five. Thanks, five. Thanks. Fight. Okay. So seven times, five times five, it's 1 75. Five times seven times five Which one? 75 five times. Five times five 1. 25. So the number off words that has one continent will be 3 50. Number of three letter words with all vowels will be 1 25. So the total number off three letter words that you conform will just be this some of this too. All right. So there will be 3 50 blesh 1 25 equal to four 175 different three letter words that can be formed under these conditions.

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