Permutations and Combination

Question

Find the number of ways for the letter of the word AUDIT to be arranged in a row so that the consonants are placed adjacent to each other.

Answer 1

DT - - -

- DT - -

- - DT -

- - - DT

 

TD- - -

- TD - -

- - TD -

- - - TD

 

Each of the above eight patterns, which are distinct based on location of the paired consonants, can be fulfilled in 3! (i.e. 6) ways, i.e. each _ _ _ _ can be filled in with vowels in 3•2•1 ways.

 

Answer is therefore 8•6 = 48