How many words can be formed each of 2 vowels and 3 consonants from the 2 letters of the given word daughter?
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Solution The given word, 'DAUGHTER' contains 3 vowels A, U, E and 5 consonants, D, G, H, T, R.Case (i) When all vowels occur together :Let us assume (AUE) as a single letter.Then, this letter (AUE) along with 5 other letters can be arranged in 6P6=(6!) ways = (6×5×4×3×2×1) ways= 720 ways.These 3 vowels may be arranged among themselves in 3 !=6 ways.Hence, the required number of words with vowels together= (6 !)×(3 !)=(720×6)=4320.Case (ii) When all vowels do not occur together.Number of words formed by using all the 8 letters of the given word= 8P8=8 !=(8×7×6×5×4×3×2×1)=40320.Number of words in which all vowels are never together = (total number of words) - (number of words with all vowels together)=(40320−4320)=36000.Question 1. How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?Solution: Nội dung chính
Question 2. How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?Solution:
Question 3. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?Solution:
So, from(i), we have, Total number of ways to select 3 girls and 4 boys = 126 x 4 = 504 Case 2: The team can consist of 4 girls and 3 boys: Total number of ways to select 4 girls and 3 boys = 4C4 x 9C3 = 1 x 84 = 84 Therefore, total number of ways to form a committee with at least 3 girls = 504 + 84 = 588 (iii) Since, the team has to consist of at most 3 girls, the team can consist of 3 girls and 4 boys, or 2 girls and 5 boys, or 1 girl and 6 boys, or 7 boys Case 1: The team can consist of 3 girls and 4 boys Total number of ways to select 3 girls and 4 boys = 126 x 4 = 504 Case 2: The team can consist of 2 girls and 5 boys Total number of ways to select 2 girls and 5 boys = 4C2 x 9C5 = = 126 x 6 = 756 Case 3: The team can consist of 1 girl and 6 boys Total number of ways to select 1 girl and 6 boys = 4C1 x 9C6 = = 84 x 4 = 336 Case 4: The team can consist of 7 boys The number of ways of selecting 7 boys out of 9 = 9C7 = = 36 Therefore, total number of ways to form a committee with at most 3 girls = 504 + 756 + 336 + 36 = 1632 Question 4. If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?Solution:
Question 5. How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7, and 9 which are divisible by 10, and no digit is repeated?Solution:
Question 6. The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?Solution:
Question 7. In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?Solution:
Question 8. Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.Solution:
Question 9. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?Solution:
Question 10. From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?Solution:
Question 11. In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?Solution:
How many different words can be formed from the letters of the word daughter?The number of words formed from 'DAUGHTER' such that all vowels are together is 4320. How many different words can be formed from the word daughter ending and beginning are consonants?1 Answer. There are eight letters in the word “DAUGHTER” including three vowels (A, U, E) and 5 consonants (D, G, H, T, R) If the vowels are to be together, we consider them as one letter, so the 6 letters now (5 consonants and 1 vowels entity) can be arranged in 6P6 = 6 ! ways. How many different eight letter words can be formed out of the word daughter so that?40320 - 4320 = 36000. How many different words can be formed from the word daughter so that ending and beginning?The total number of words formed from 'DAUGHTER' such that no vowels are together is 14400. ⇒nPr=n! n−r! Where n=total number of things and r=no. How many different words can be formed from the word daughter so that ending and beginning letters are Consonents?= 40320`. How many words can you make out of daughter?189 words can be made from the letters in the word daughter. Can be formed from the letters of the word daughter?Solution : The letters of the word daughter are “d,a,u,g,h,t,e,r”. How many words can be formed each of 2 vowels and 3 consonants from the letters of the given word daughter *?Therefore, 30 words can be formed from the letters of the word DAUGHTER each containing 2 vowels and 3 consonants.
How many different words can be formed each containing 2 vowels and 3 consonants?=6800×120=816000.
How many words are possible with 2 vowels and 2 consonants?"Number of words each consisting of two vowels and two consonants which can be made out of the\netters of the word 'DEVASTATION is\nA) 126" Was this answer helpful?
How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word shoulder?Solution 1
Each of these 30 combinations of 2 vowels and 3 consonants can be arranged among themselves in 5! ways.
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