How many words can be formed out of the letters of the word banana so that the consonants occupy the even places?
Solution : In word ARTICLE, there are `3` vowels and `4` consonants. Show
View Discussion Improve Article Save Article View Discussion Improve Article Save Article How many distinguishable permutations of the letters in the word BANANA are there ? The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is 144. Explanation: Total number of letters in the ‘ARTICLE’ is 7 out which A, E, I are vowels and R, T, C, L are consonants Given that vowels occupy even place ∴ Possible arrangement can be shown as below C, V, C, V, C, V, C i.e. on 2nd, 4th and 6th places Therefore, number of arrangement = 3P3 = 3! = 6 ways Now consonants can be placed at 1, 3, 5 and 7th place ∴ Number of arrangement = 4P4 = 4! = 24 So, the total number of arrangements = 6 × 24 = 144. How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places? SolutionThe word ARTICLE consists of 3 vowels, which have to be arranged in 3 even places. This can be done in 3! ways. Concept: Factorial N (N!) Permutations and Combinations Is there an error in this question or solution? APPEARS INNo worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses Solution The correct option is B 144The word ARTICLE consists of 3 vowels that have to be arranged in the three even places. This can be done in 3! ways.And, the remaining 4 consonants can be arranged among themselves in 4! ways. (adsbygoogle = window.adsbygoogle || []).push({}); ∴ Total number of ways = 3!×4!=144How many words can be formed out of the letters of the word ARTICLE so that vowels occupy the even places?Answer Verified Hint: 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: We have to arrange the vowels (A, I, and E) in even places. Note: If the question was asked to arrange the consonants, we will choose the 4 consonants at odd places in\[4!\] ways and then arrange vowels. How many words can be formed out of the letters of the word BANANA so that the consonant occupy the even places?So 60 distinguishable permutation of the letters in BANANA.
How many words can be formed so that the vowels occupy the even places?Solution. The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is 144.
What is the number of ways of arranging the letters of the word BANANA so that no two ends appear together?The number of arrangements of the letters of the word 'BANANA' in which the two N's do not appear adjacently is 40.
How many words can be formed in letters of i so the vowels always come together II the vowels never come together?Total no. of words formed=4×24×6=576.
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