What is the number of possible words that can be made using the word quiz such that vowels never come together?

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  • Find all the possible scenarios where vowels come together and subtract it from the total words possibleThe word LETTER has 6 alphabets of which 2 are repeated twice.The total number of 6 letter words =6!2!2!=6×5×4×3×22×2=180 wordsThere are 2 vowels in the word LETTER, that is, (EE).If EE are assumed to be together they can be arranged in 5!2! ways.So, the words where vowels are together are 5!2!=1202=60 Thus, the total number of words where vowels are not together=180-60=120Hence, there are 120 words formed from the word LETTER where no vowels are together.
  • Find the number of words, with or without meaning, that can be formed with the letters of the word ‘CHAIR’.
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  • Permutation Find the number of words ,with or without meaning,that can be formed with the letters of the word “CHAIR”.
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  • What is an example of a permutation?
  • What is the number of possible words that can be made using the word quiz such that the vowels never come together?
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Solution

Find all the possible scenarios where vowels come together and subtract it from the total words possibleThe word LETTER has 6 alphabets of which 2 are repeated twice.The total number of 6 letter words =6!2!2!=6×5×4×3×22×2=180 wordsThere are 2 vowels in the word LETTER, that is, (EE).If EE are assumed to be together they can be arranged in 5!2! ways.So, the words where vowels are together are 5!2!=1202=60 Thus, the total number of words where vowels are not together=180-60=120Hence, there are 120 words formed from the word LETTER where no vowels are together.

  • School Cebu Technological University (formerly Cebu State College of Science and Technology)
  • Course Title ENGINEERIN 123
  • Pages 1

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1. Find the number of words, with or without meaning, thatcan be formed with the letters of the word ‘CHAIR’.2. Find the number of words, with or without meaning, thatcan be formed with the letters of the word ‘INDIA’.3. Find the number of words, with or without meaning, thatcan be formed with the letters of the word ‘SWIMMING?4.How many different words can be formed with the lettersof the word ‘SUPER’ such that the vowels always cometogether?5.Find the number of different words that can be formedwith the letters of the word ‘BUTTER’ so that the vowels are

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Solution : (i) The given word 'AGAIN' consists of 5 letters, out of which there are 2 A's and the rest are all distinct.<br> Hence, the number of words formed by using all the letters of the given word =`(5!)/(2!)`=60. <br> (ii) When the letters of the word 'AGAIN' are listed in a dictionary, the first word would be AAGIN. <br> Starting with A and arranging the remaining 4 letters A, G, I, N, we oibtain 4 ! words, i.e., 24 words. <br> The 25th word would be GAAIN, which starts with G.<br> Now, starting wilth G arrange the remaining 4 letters AAIN,(in which A occurs 2 times and the rest are different) in all possible ways.<br> Number of such arrangements =`(4!)/(2!)`=12. <br> Thus, we obtain 12 new words. <br> The 37th word would be IAAGN, which starts with I. Now, starting with I and arranging the remaining 4 letters, <br> AAGN, we get `(4!)/(2!)`=12 words. <br> The 49th word would be NAAGI and hence the 50th word is NAAIG.

What is the number of possible words that can be made using the word quiz such that vowels never come together?

Find the number of words, with or without meaning, that can be formed with the letters of the word ‘CHAIR’.

This is a List of Available Answers Options :

  1. 5
  2. 3125
  3. 120
  4. 25

The best answer is C. 120.

Reported from teachers around the world. The correct answer to ❝Find the number of words, with or without meaning, that can be formed with the letters of the word ‘CHAIR’.❞ question is C. 120.
I Recommend you to read the next question and answer, Namely Permutation, Combination, or Neither?A team of 8 basketball players need to choose a co-captain and captain. How many ways can these positions be filled?  with very accurate answers.

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answered

Permutation Find the number of words ,with or without meaning,that can be formed with the letters of the word “CHAIR”.

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BenjaminNotFound BenjaminNotFound

Solution: 'CHAIR' contains 5 letters. Therefore, the number of words that can be formed with these 5 letters = 5! = 5*4*3*2*1 = 120.

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A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}.

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