if all the letters of word engineer be written at random,what is the probability that all the letters e are found together

First, what's the probability that all three E's will start the word? The word has 8 letters, of which three are E's, so the chance of the first letter being an E is 3/8. The chance of the first two letters both being E's is 3/8 x 2/7. And the chance of all three E's being together to start the word is 3/8 x 2/ 7 x 1/6. However, you are interested in the 3 letter combo occurring anywhere, meaning it could be letters 1, 2 &3, or 2,3, & 4, or... or 6, 7 & 8. So there are 6 ways that you can have all three E's together. So final answer is:

6 x 3/8 x 2/7 x 1/6