Question

The letters of the word COMPUTER are written on separate sheets of paper and placed in a hat. Three letters are then randomly drawn from the hat, one after the other and without replacement. Find the probability that all 3 letters are vowels using this method: P(3 vowels) = number of 3-letter words having 3 vowels/number of 3-letter words.

Answer 1

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