Arranging the Letters of a Word where all the letters are different

Problem 1

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.
Solution Ans :
1
8
,
1
8
,
1
56

Problem 2

The letters of the word ORIENTAL are arranged in all possible ways. Find the probability and odds of getting an arrangement which starts with a vowel and ends with a consonant.
Solution Ans :
2
7
, 16 : 55, 55 : 16

Problem 3

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
Solution Ans :
1
273
, 1 : 272, 272 : 1,
272
273

Problem 4

Define the Event and identify the number of favourable choices in the following cases
  1. 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
  2. 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.
  3. The letters of the word RIGHTEOUSLY are arranged in a row at random. Find the probability that the even places are filled with consonants.
  4. 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 is
  5. The letters of the word TROPICAL are arranged in a row at random. Find the probability that no two vowels may come together.
Solution Ans : 1; 43,200; 18,14,400; 7,200; 14,400

Practice Problems

  1. The letters of the word QUESTION are arranged in a row at random. The probability that the word so formed starts with T and ends with N is
  2. The letters of EQUATION are arranged in all positive ways. Find the probability of getting an arrangement which start with an vowel and ends with a consonant.
  3. The letters of the word CONJUGATED are arranged at random. The probability that all the consonants come together.
  4. The letters of the word PRUDENTIAL are arranged in a row at random. The probability that there are exactly two letters between D and A.
  5. The letters of the word WRESTLING are arranged in a row at random. The probability that the vowels may be in even places is
  6. The letters of the word QUACKERY are arranged at random. Find the probability that the odd places are occupied by constants.
  7. The letters of the word IMPORTANCE are arranged at random. Find the probability that the vowels do not come together.
Author : The Edifier
Page PS11