Answer: A)
There are 8 different letters in the given word "XANTHOUS", out of which there are 3 vowels and 5
consonants.
Let us mark these positions as under:
[1] [2] [3] [4] [5] [6] [7]
Now, 3 vowels can be placed at any of the three places out of 4 marked 1, 3, 5, and 7.
Number of ways of arranging the vowels = 4P3
= 24 ways.
Also, the 5 consonants at the remaining positions may be arranged in 5P5 ways = 5! Ways
= 120 ways.
Therefore, required number of ways = 24 x 120 = 2880 ways.