# 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

- the two R's come together
- the two R's do not come together
- the two R's and the two A's come together
- the two R's come together and the two A's do not come together

# Problem 5

Define the Event and identify the number of favourable choices in the following cases

- What is probability that 4 I’s appear consecutively in the word MISSISSIPPI assuming that the letters are arranged at random
- Find the probability that in a random arrangement of the letters of the word UNIVERSITY, the two I’s do not come together.
- 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.
- 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

# Practice Problems

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

Author : The Edifier