AP EAMCET202018 Sep 2020Morning ShiftMathematicsPermutation and CombinationActual
The number of different words that can be formed from the letters of the word "INTERMEDIATE" such that two vowels never come together, is
Options
- A( 6 ! 2 ! 7 ! 2 ! 3 ! )
- B( 5 ! 2 ! 6 ! 3 ! )
- C(6 ! 7 ! 2 ! 3 ! )
- D( 6 ! 2 ! 6 ! 2 ! 3 ! )
Correct answer
A. ( 6 ! 2 ! 7 ! 2 ! 3 ! )
Step-by-step solution
In the given word "INTERMEDIATE" the vowels and consonants are IEEIAE and NTRMDT respectively. Now number of ways to arrange consonants first is ( 6 ! 2 ! ). Now number of ways to arrange six vowels in the seven available and favourable positions are ( ^7 P₆ 3 ! 2 ! = 7 ! 3 ! 2 ! ) So number of required arrangements (= 6 ! 2 ! 7 ! 2 ! 3 ! )