The letters of the word LOGARITHM are arranged at random. Find the probability that: vowels are never 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.

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

Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement: starting with a vowel and end with a consonant.

In how many ways can the letters of the word ARRANGEMENTS be arranged? : Find the probability that the consonants are together.