INTERMEDIATE : Not talking about Level. Part-V
I N T E R M E D I A T E How many words can be made with the letters of the word I N T E R M E D I A T E if the relative order of vowels and consonants does not change?
The answer is 21600.
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1 solution
@Kalash Verma how did you do it?
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Similar , to the given given solution.
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But when does it take into account the fact that the relative order has to be the same.
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@Adarsh Kumar – The relative order of vowels and consonants doesn't change when vowels occupy the places of vowels and consonants occupy the places of consonants.
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@A Former Brilliant Member – Ok,now I get it,what is the meaning of relative order?
Ok,why is this wrong?First,we choose 6 places out of 12,for the vowvels,then arrange them which can be done only in one way(IEEIAE),then there is only one way to choose the 6 places for the consonants and only one way to arrange them.
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@Adarsh Kumar – This will be right when it is asked that relative position of vowels and consonants doesn't change.U should ask @Sandeep Bhardwaj sir he should be able to make it more clear.
@Adarsh Kumar – Relative order of vowels and consonants doesn't change means vowels always occupy the places of vowels and consonants always occupy the places of consonants.
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@Sandeep Bhardwaj – Sir please see to the following word and tell me weather it is correct with respect to the question.
ENTERMADIITE.
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@A Former Brilliant Member – Yeah, its correct.
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@Sandeep Bhardwaj – Thanks sir !Now I do not have any doubt in ur 'intermediate set'
@Sandeep Bhardwaj – Okkk,Sir got it,thanx a lot!
There are 6 consonants and 6 vowels, so we have two groups of letters. Firstly, vowels can be placed at 6 different positions, but there are two I and three E, so the possible ways are equal to 2 ! 3 ! 6 ! Similarly, for the consonants, there are 6 different places, and there are 2 T, so the possible ways are equal to 2 ! 6 !
Therefore, the total words can be made equal to 2 ! 3 ! 6 ! × 2 ! 6 ! which is 2 1 6 0 0