Number of 3-letter words having 3 vowels = 3! = 3 * 2 * 1 Total number of 3-letter words is $8P3=\frac{8!}{(8-3)!}=8\times 7\times 6$ $P(all\ 3\ vowels)=\frac{3\times 2 \times 1}{8\times 7\times 6}=You\ can\ calculate$