How many words can be formed with the letters of the word harayana if vowel are together?
How many words can be formed from the letters of the word ‘DAUGHTER’ so that(i) The vowels always come together?(ii) The vowels never come together? Show
Answer Verified
Hint: The word daughter has $8$ letters in which $3$ are vowels. For the vowels to always come together consider all the $3$ vowels to be one letter (suppose V) then total letters become $6$ which can be arranged in $6!$ ways and the vowels themselves in $3!$ ways.Complete step-by-step answer: (ii)We have to find the number of words formed when no vowels are together. Note: Combination is used when things are to be arranged but not necessarily in order. Permutation is a little different. In permutation, order is important. Permutation is given by- (i) The given word ' HARYANA' consists of 7 letters, out of which there are 1 H, 3 A's, 1 R, 1 Y and 1 N. Total number of words formed by all the letters of the given word = 7 !3!=840. (ii) Let us consider as a single letter.Now, + ARYAA will give us 6 letters out of which there are 3 A' s, 1 R, 1 Y and 1 .Total number of all such arrangments = 6 !3!=120. But, H and N can be arranged amost themselves in 2! ways. Hence, the number of words having H and N together = (120×2)=240. (iii) After fixing H in first place and N in last place, we have 5 letters, out of which there are 3 A' s, 1 R and 1 Y. Hence, the number of words beginning with H and ending with N=5 !3!=20. (iv) The given word contains 3 vowels AAA and let us treat as 1 letter.Now, we have to arrange 5 letters HRYN+ at 5 places.Hence, total number of words formed having all vowels together = 5 !=(5×4×3×2×1)=120. How many words can be formed with the letters of the word Haryana how many of these have 3 vowels together?Hence, total number of words formed having all vowels together = 5 ! =(5×4×3×2×1)=120.
How many words can be formed such that all vowels are together?⇒ The total number of words formed=6! ×3! The number of words formed from 'DAUGHTER' such that all vowels are together is 4320.
How many words can be formed from the letters of the word after so the vowels never come together?Number of ways when vowels are never together =120−48=72.
How many different words can be formed with the letters of the word Haryana If word with H and end with n?7x6x5x4= 840; which is the total no. of different words that can be formed from the letters of the word Haryana. 5x4= 20; which is the no. of words that begin with H and end with N.
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