Permutations and Combination quesitons

Question 1: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

Question 2: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

Question 3:What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?

Question 4: There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

Question 5: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?

Question 6: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

Question 7: Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

Question 8: In how many ways can the letters of the word "PROBLEM" be rearranged to make seven letter words such that none of the letters repeat?