If the letters of the word 'REGULATIONS' be arranged at random what is the probability that there will be exactly 4 letters between R and E?

The letters of the word 'EQUATION' are arranged in a row. Find the probability that: all the vowel are together.

The letters of the word LOGARITHM are arranged at random. Find the probability that: exactly 4 letters etween G and H.

The letters of the word LOGARITHM are arranged at random. Find the probability that: begin with O and end with T.

If the letters of the word PROBABILITY are written down at random in a row, the probability that two B-s are retogether is

The letters of the word 'EQUATION' are arranged in a row. Find the probability that: Arrangement starts with a vowels and ends with a consonant.