Arranging the letters of a word where all the letters are different

Brief

Define the Event and identify the number of favourable choices in the following cases
a) Each of the letters A, B, E, L, T are written on a separate card. If all the cards are arranged in a row in all possible ways, the probability of the forming the word TABLE is

Short

The letters of the word TRIANGLE are arranged at random. Find the probability and odds that the word so formed (i) starts with T (ii) ends with R (iii) starts with T and ends with R.
The letters of the word ‘ORIENTAL’ are arranged in all possible ways. Find the probability and odds of getting an arrangement which starts with an vowel and ends with a consonant.
In a random arrangement of the letters of the word “UNCOPYRIGHTABLE”. Find (a) the probability and odds that all the vowels come together and (b) the probability that the vowels do not come together
The letters of the word SLAUGHTER are arranged in a row at random. Find the probability that the vowels may be in the odd places.
The letters of the word "RIGHTEOUSLY" are arranged in a row at random. Find the probability that the even places are filled with consonants.
The letters of the word TROPICAL are arranged in a row at random. Find the probability that no two vowels may come together.
The letters of the word “PENTAGON” are arranged in a row at random. Find the probability that there are exactly two letters between E and A
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