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Using the letters of the word 'EDUCATION' how many words using 6 letters can be made so that every word contains at least 4 vowels?
vowels = {EUAIO}consonents = {DCTN} words with Atleat 4 vowels = {exactly 4 vowels and 2 consonents} + {exactly 5 vovels and 1 consonent}= 5C4*4C2 + 5C5*4C1=5*6 + 1*4=30 + 4=34
vowels = {EUAIO}consonents = {DCTN} words with Atleat 4 vowels = {exactly 4 vowels and 2 consonents} + {exactly 5 vovels and 1 consonent}= 5C5*4C1*6factorial + 5C5*4C*6factorial= 24480In case one combination selects all the combination of 4 vowels and combination of 2 consonents then we use permutation to get all the shuffled 6 letter word with 4 vowels and 2 consonentsSimilarly case 2
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