Number of words that can be formed with the letters of the word A L G E B R A so that all the vowels are separated (or no two vowels come together) is

Step-by-step solution

Vowels are A , E , A Consonants are L , G , B , R X L X G X B X R X Since there is no restriction on consonants, we must place them first and they can be arranged in 4 ! = 24 days. Now to arrange vowels so that no two of them are together we have 5 places X . Out of these 5 places, 3 can be selected in 5 C 3 ways and then one arrangement can be made in 3 ! 2 ! ways. Thus, required ways = 4 ! × 5 C 3 × 3 ! 2 ! = 720