Algebra> Using the letters of the word 'EDUCATION'...

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?

Vikash Yadav , 8 Years ago

Grade 11

2 Answers

Ritesh Khatri

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

Last Activity: 8 Years ago

Waris

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

Last Activity: 7 Years ago