Arranging the Letters of a Word where all the letters are not different

Problem 1

The letters of SUCCESS are arranged at random. The probability that the vowels occupy even places is
Solution Ans :
1
7

Problem 2

In a random arrangement of the letters of the word COMMERCE. Find the probability that all the vowels come together
Solution Ans :
3
28

Problem 3

If the letters of the word ASSASSINATION are written down at random in a row, the probability that no two S's occur together is
Solution Ans :
42
143

Problem 4

The letters of the word ARRANGE are arranged at random. Find the probability that
  1. the two R's come together
  2. the two R's do not come together
  3. the two R's and the two A's come together
  4. the two R's come together and the two A's do not come together
Solution Ans :
2
7
,
5
7
,
2
21
,
4
21

Problem 5

Define the Event and identify the number of favourable choices in the following cases
  1. What is probability that 4 I’s appear consecutively in the word MISSISSIPPI assuming that the letters are arranged at random
  2. Find the probability that in a random arrangement of the letters of the word UNIVERSITY, the two I’s do not come together.
  3. The letters of the word ACCOUNTANCY are arranged in a row at random. Find the probability that (i) all c’s come together and (ii) all c's come together and all a's may not come together.
  4. When all the letters of the word EAGLET are arranged in a row, that probability of getting a word in which E’s occupy central position is
Solution Ans :
2
7
,
5
7
,
2
21
,
4
21

Practice Problems

The probability that in a random arrangement of letters of the word COLLEGE the two E’s do not come together is
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