How many different words can be formed from the letter of the word combine so that vowels always remain together?
|
Show
Solution There are 7 letters in the word. STRANGE, including 2 vowels (A, E) and 5 consonants (S, T, R, N, G). (i) Considering 2 vowels as one letter, we have 6 letters which can be arranged in 6P6 = 6! ways A, E can be put together in 2! ways. Hence, required number of words = 6!×2! = 6×5×4×3×2×1×2 = 720×2 = 1440. (ii) The total number of words formed by.: using all the letters of the words 'STRANGE'is 7P7=7! = 7×6×5×4×3×2×1 = 5040. So, the total number of words in which vowels are never together = Total number of words - number of words in which vowels are always together = 5040-1440 =3600 (iii) There are 7 letters in the word 'STRANGE', out of these letters 'A' and `E' are the vowels. There are 4 odd places in the word 'STRANGE'. The two vowels can be arrangd in 4P2 ways. The remaining 5 consonants can be arranged among themselves in 5P5 ways. The total number of arrangements. = 4P2×5P5 = 4!2!×5! = 1440
COMBINE HAS 7 LETTERS in which C,M,B,N R 4 CONSONANTS ND O,I,E R 3 VOWELS 1) OIE, C,M,B,N CAN BE ARRANGED 5!=120 ways bt vowels can be arranged among themselves=3!=6 ways total no.of ways=120*6=720
COMBINE HAS 7 LETTERS in which C,M,B,N R 4 CONSONANTS ND O,I,E R 3 VOWELS 1) OIE, C,M,B,N CAN BE ARRANGED 5!=120 ways bt vowels can be arranged among themselves=3!=6 ways total no.of ways=120*6=720 Zigya App Solution not provided. Ans. (i) 720 (ii) 1440 (iii) 576 166 Views Permutations and CombinationsHope you found this question and answer to be good. Find many more questions on Permutations and Combinations with answers for your assignments and practice. Explore. Zig In MathematicsBrowse through more topics from Mathematics for questions and snapshot. Explore. Zig In How many different words can be formed with the letters of the word combine vowels always remain together?The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI).
...
Discussion :: Permutation and Combination - General Questions (Q. No. 2). How many different words can be formed of the letters of the word combine so that vowels may occupy odd places?In order that the vowels may occupy odd places, we first of all arrange any 3 consonants in even places in 4P3 ways and then the odd places can be filled by 3 vowels and the remaining 1 consonant in 4P4 ways. So, Required number of words = 4P3 × 4P4 = 24 × 24 = 576.
How many different words can be formed using the letters of the word combine?64 words can be made from the letters in the word combine.
How many different ways can the letters of the word combine be arranged so that the vowels always come together Write your answer here?This gives the number of possible arrangements as 3*2*1 = 6. In all there are 24*6 = 144 ways of arranging the letters. The required number of arrangements that satisfy the condition that vowels and consonants are not together is 144.
|
