How many words can be formed using all the letters of the word failure so that consonants occupy odd positions?
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Check out the new look and enjoy easier access to your favorite features Answer VerifiedHint: Find the number of vowels and consonants in the word ‘ARTICLE’. Arrange them in even and odd places as there are a total 7 letters in the word. So arrange them in 7 places and find how the 7 letters can be arranged. Complete step-by-step answer: Consider the word given ‘ARTICLE’.Total number of letters in the word ARTICLE = 7.Number of vowels in the word = A, I and E =3.Number of consonants in the word = R, T, C and L = 4.There are 7 places amongst which the vowel has to be arranged in an even place.We have to arrange the vowels (A, I, and E) in even places.It can be done in \[3!\] ways.We have to arrange the consonants (R, T, C, and L) in odd places. It can be done in \[4!\] ways.\[\therefore \]We can arrange the 7 letters in \[\left( 3!\times 4! \right)\]ways.\[\left( 3!\times 4! \right)=\left( 3\times 2\times 1 \right)\times \left( 4\times 3\times 2\times 1 \right)=6\times 24=144\].\[\therefore \] We can form 144 words with the letters of the word ARTICLE where vowels occupy the even places and consonants the odd places.
Discussion :: Permutation and Combination - General Questions (Q.No.10)
How many ways can be letters of the word failure be arranged so that the consonants may occupy only odd places *?As a result, there are 576 different ways to arrange the consonants so that they only appear in odd positions.
How many words can be formed with the letters of the word failure in which consonants may occupy even places?Total no. ways =24×24=576 ways.
How many words can be formed out of the letters of the word failure?Therefore, there are 360 words that can be formed using the letters of the word FAILURE so that F is not included in any word.
How many words can be formed of the letters in a word failure such that no two consonants are together?Answer is 576. There are seven letters in the word 'FAILURE' out of which the consonants are- F, L and R.
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