Question

Using the letters of he word ‘EDUCATION’ how many words using 6 letters can be made so that every word contain atleast 4 vowels?

Answer 1

Given 

letter = EDUCATION 

Vowels = A,E,I,O,U 

Consonants = D,C,T,N 

There will be two possibilities 

= 2 consonants + 4 vowels and 1 consonants + 5 vowels 

Hence, 

total words = (⁴P₂ × ⁵P₄) + (⁴P₁ × ⁵P₅) 

= (5 × 4 × 3 × 2 × 4 × 3) + (5 × 4 × 3 × 2 × 1 × 4) 

= 1440 + 480 

= 1920