In how many different ways can the letters of the word ‘CANDIDATE’ be arranged in such a way that the vowels always come together
Explanation:
There are 9 letters in the given word out of which 4 are vowels.
In the word 'CANDIDATE' we treat the vowels 'AIAE'as one letter.
Thus, we have 'CNDDT (AIAE)'
Now, we have to arrange 6 letters, out of which D occurs twice.
Therefore, number of ways arranging these letters = 61/21
= 6×5×4×3×2×1/2×1=720/2=360 ways
Now, AIAE has 4 letters in which A occurs 2 times. Number of ways of arranging these letters
=41/21=4×3×2×1/2×1=12
Therefore, required number of wyas
= 360×12=4320
