Question

How many five-letters containing 2 vowels and 3

consonants can be formed using the letters of the word

EQUALITY so that 2 vowels occur together?​

Answer 1

Answer:

Separate out Vowels and Consonants

Vowels - a, e, i, u ----4

Consonants - q, l, t, y ----4

Ways to find 2 vowels together

Choose 2 vowels in 4C2 ways, but order is important so 4C2*2=4*3

Placing vowels in the word

Now take two vowels together as one letter, so we have to find 4 letter word, wherein one of 4 place is taken by two vowels..

_, _, _, _

So, the place can be taken in 4C1 ways - 4 ways

Placing consonants in the word

there are 3 places for consonants and the order matters, so 4*3*2 -- 24 ways

Total ways = 12*4*24=1152