Determine the number of ways of arranging the letters in the word handle
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Determine the number of ways of arranging the letters in the word handle if a) there are no restrictions b) the first letter must be a consonant c) the second and fifth letters must be vowels
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- a)How many four letter words including non-sense word can be formed from the word "BEAUTIFUL" if letters cannot be repeated? b) How many of the four letter words (from part a) begin with a vowel? c) How many of the four letter words (from part a) begin and end with a consonant?The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain:a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?6. Find the act values of the following a)-135) b) ta
- The Martian language can be written in the familiar Roman alphabet, which has 21 consonants (B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z) and 5 vowels (A, E, I, O, U). All Martian nouns begin with a consonant, followed by one or more vowel-consonant pairs. However, no consonant can appear more than once in a single noun, and no vowel can appear more than once in a single noun. For example, VUX, DIYOK, and ZOBALUT are possible Martian nouns, but X, VUV, DIYIK, and ZEZELAL are not. How many Martian nouns are possible? Your answer must be a number. Briefly explain your answer. Recent expeditions to Mars have cast doubt on whether the Martian language can be written with exactly 21 consonants and 5 vowels. Suppose that Martian requires c consonants and v vowels, where c > 0, v > 0, and c > v. Express the number of possible Martian nouns in terms of c and v. Your answer need not be in closed form.Sammy's Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three bottles of salsa, weighs the contents, and tastes the product. Help Sammy select the sample jars. Today's cases are coded 07N61 through 07N80. Complete parts a) through c) below. a) Carefully explain your sampling strategy. Choose the correct answer below. OA. Select one jar randomly from each case. B. Select the most convenient case. Then select the first three jars from the case. OC. Select three cases at random. Then select one jar randomly from each case. OD. Select one case at random. Then select three jars randomly from the case. b) Show how to use random numbers to pick the three jars for testing. Choose the correct answer below. A. Use random numbers to choose one case from numbers 61 through 80. Then use random numbers between 1 and 12 to…If A = {vowels} and B {letters in the word “spare"}, = find: a) N{A} b) N{B} c) N(AN B) d) N(AUB)
- In how many ways can all of the letters in the word ISOSCELES be arranged if the arrangement must: a) start with E and end with E b) Have S for the middle letter c) have the vowels togrther d) have the consonants together e) ha ve the consonants and vowels alternateMajor League Baseball teams maintain a 25- man roster and also a 40- man roster. Players on the 25- man roster may play in official games throughout the season. The additional 15 players on the 40- man roster may play in games starting September 1. a) how many 9-player batting orders are possible from a 25-man roster? b) How many 9-player batting orders are possible from a 40-man roster?The English alphabet contains 21 consonants and five vowels. How many strings of six lowercase letters of the English alphabet contain 1. a) exactly one vowel? b) exactly two vowels? c) at least one vowel? d) at least two vowels?
- Nine stuffed animals, all different, are placed along baby’s toy shelf. How many possible arrangements are there if:Many newspapers contain jumble puzzles, where the letters of a word are given out of order. For the jumble puzzle LETTHUS, find the following. a) Determine the number of possible arrangements of the letters given. b) What is the unjumbled form of the word?
