How many ways can a consonant and a vowel be chosen out of the letters of the word logarithm?
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How many words with or without meaning can be formed using all the letters of the word "EQUATION" at a time if vowels and consonants occur together. My answer is $5!3!2!=1440$. Am I right?
asked Sep 12, 2015 at 14:47
$\endgroup$ 1 $\begingroup$ In the word "EQUATION" there are 3 consonants (Q,T,N) so there are $3!$ ways to arrange and 5 vowels (E,U,A,I,O) so $5!$ ways to arrange. In whole for both first consonant and then vowels or vice-versa, there are $2!$ ways . so in total $2! \cdot 5! \cdot 3!=1440$ ways. answered Jun 15, 2017 at 4:39
$\endgroup$ 1 Answer Verified
Hint – Pick out the vowels and consonants separately from the given word ‘COURAGE’ and use the combination formula for selecting r dissimilar things out of total n things Note- In English alphabet set we have in total 27 alphabets which can broadly be classified into two categories that are vowels and consonants. (A, E, I, O, U) are the vowels while rest are marked as consonants. ADDITIONAL QUESTION BANK Q.58 Correct Try again Try again Try again The word `LOGARITHM’ consist of 9 letters,in which there are 6 consonantes and 3 vowels. The selection of a consonant from 6 consonants in done in 6C1 = 6 ways. while selection of a vowel out 3 vowels is done by 3 different way. The letters of the word LOGARITHM are arranged at random. Find the probability that start with vowel and end with ends with consonant. SolutionThere are 9 letters in the word LOGARITHM. ∴ P(E) = `("n"("E"))/("n"("S")` = `(3 xx 7! xx 6)/(9!)` Concept: Elementary Properties of Probability Is there an error in this question or solution? APPEARS IN
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Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Related Videos160635 37 7.8 K 1:37 In how many ways can a consonant and a vowel be chosen out of the letters of the word `LOGARITHM` 643295511 0 8.8 K 2:26 A word consists of 9 letters: 5 consonents and 4 vowels. Three letters are chosen at random. In how many ways can these 3 letters be chosen. 25873 15 4.6 K 1:55 in how many ways can a consonant and a vowel can be chosen out of the words of 'COURAGE'. 61736571 100 400 1:31 In how many ways can a vowel, a consonant and a digit be chosen out of the 26 letters of the English alphabet and the 10 digits? 646642511 0 300 4:09 'ALGEBRA' शब्द के अक्षरों को कितने प्रकार से व्यवस्थित किया जा सकता है जिसमें व्यंजन (consonants) और स्वर (Vowels) अक्षरों के सापेक्ष स्थान (relative position) में कोई बदलाव न हो ? 116068044 81 7.6 K 3:21 If 5 vowels and 6 consonants are given, then how many 6 letter words can be formed with 3 vowels and 3 consonants. Show More Comments Add a public comment... Follow Us: Popular Chapters by Class: Class 6 AlgebraBasic Geometrical IdeasData HandlingDecimalsFractions Class 7 Algebraic ExpressionsComparing QuantitiesCongruence of TrianglesData HandlingExponents and Powers Class 8 Algebraic Expressions and IdentitiesComparing QuantitiesCubes and Cube RootsData HandlingDirect and Inverse Proportions Class 9 Areas of Parallelograms and TrianglesCirclesCoordinate GeometryHerons FormulaIntroduction to Euclids Geometry Class 10 Areas Related to CirclesArithmetic ProgressionsCirclesCoordinate GeometryIntroduction to Trigonometry Class 11 Binomial TheoremComplex Numbers and Quadratic EquationsConic SectionsIntroduction to Three Dimensional GeometryLimits and Derivatives Class 12 Application of DerivativesApplication of IntegralsContinuity and DifferentiabilityDeterminantsDifferential Equations Privacy PolicyTerms And Conditions Disclosure PolicyContact Us How many ways can a consonant and a vowel be chosen out of the letters of the word courage?Now in the given word 'COURAGE' there are 3 consonants that are (c, r, g) and there are 4 vowels that are (o, u, a, e). So out of 3 consonants a single consonant can be chosen in 3C1ways.
How many ways vowels and consonants are together?total number of ways consonant and vowel can be chosen is 4×3=12 ways.
How many ways can a vowel a consonant and a digit be chosen out of the 26 letters of the English alphabet and the 10 digits?Total number of ways to choose one vowel, one consonant and one digit is 1050.
How many of the arrangements of the letter of the word logarithm?Solution. There are 9 letters in the word LOGARITHM. These letters can be arranged among themselves in 9P9 = 9! ways.
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