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DcteepePreviousProblem ListNext(1 point) What is the probability that if 9 letters are typed no letters are repeated?The probability that no letters are repeated i5...

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DcteepePreviousProblem ListNext(1 point) What is the probability that if 9 letters are typed no letters are repeated?The probability that no letters are repeated i5Preview My AnswersSubmit AnswersYou have attempted Inis problem times You have unlimited attempts remainingEmail instructorPage WeBWork - 1926-2016 ticniPar]

Dcteepe Previous Problem List Next (1 point) What is the probability that if 9 letters are typed no letters are repeated? The probability that no letters are repeated i5 Preview My Answers Submit Answers You have attempted Inis problem times You have unlimited attempts remaining Email instructor Page WeBWork - 1926-2016 ticni Par]



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If a five-letter word is formed at random (meaning that all sequences of five letters are equally likely), what is the probability that no letter occurs more than once?

Appropriate 27 on the mental counting principle if one event cannot care in, in and in ways and the second event occurred in in way. So the number off way that the two events can occur in sequence it then M times and okay, eso There is 26 possible letters and those each letter in five letters World has 26 possible the choices so reducing the fundamental Okay, the fundamental probabilities for the number when 2016 2016 2016 2016, 26 which is equal to 11,000 818 a one 376 So there is 1,100,000 88 1776 different students off five letters is a little or unique when the first lady has 26% of choices and second picture is 25. To hear the number is equal toe 26 times 25 20 support 23 times went through, which is it was 27 million. Ah, ain't mine to be six view view And this without replacement eso there in 8 7,000,009, 36 years here different sequence off. Five letters were no later. Okay, more than one and the probability is the number off paper will outcome divided by the number off versatile. So therefore, you know, no letter appear more than once is able to the number off favor will outcome. Which a several million? 8936 years you over the number off. But our country is 11 million 88 1 27 6 There's hundreds, so the percentage it would do, 66.4%.

Okay, so we're given the word mathematics and were asked to find the probability that if we pick some letter of random that we'll get a letter that occurs more than once in this in this word here. So first we total it out. The total number of letters and mathematics is 11. So that goes in the denominator. And now we're gonna find the letters that occur more than once We have m. So there's those two A's occur more than once Ti's also occur more than once and then h is a single letter. So we don't include that one. We have e That does not occur more than once I see an s also. So we have a total of 123456 So we get six out of 11 and when we divide that, we get 0.5 for 54 So this repeats here. And when we multiplied by 11 we get 50 or sorry. When we multiplied by 100 I got this 11 in my brain we multiply by 100 to find the percentage we get 54.5%

Okay, so here we've got six letters that we can use to form random four letter words, and we want to know the probability of forming a word with no vowels in it. It's the best. We can't have a A's or ease. So the probability of picking this first letter to be a non vowel it's just gonna be for over six. And since we can allow repeating letters, the probability of the second letter being a non vowel is also just going to be for over six, which is the same as the third and the fourth. Um so our final answer will just before to the power of for divided by six to the power of four, which gives us the value of 0.1 975

Okay, so here we've got six letters that we can use to form random four letter words, and we want to know the probability of forming a word with no vowels in it. It's the best. We can't have a A's or ease. So the probability of picking this first letter to be a non vowel it's just gonna be for over six. And since we can allow repeating letters, the probability of the second letter being a non vowel is also just going to be for over six, which is the same as the third and the fourth. Um so our final answer will just before to the power of for divided by six to the power of four, which gives us the value of 0.1 975


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