Conditional probability in arrangements

A question is this type if and only if it asks for a conditional probability given information about an arrangement (e.g., 'probability given that certain items are together').

2 questions

CAIE S1 2023 June Q3
3
  1. Find the number of different arrangements of the 8 letters in the word COCOONED.
  2. Find the number of different arrangements of the 8 letters in the word COCOONED in which the first letter is O and the last letter is N .
  3. Find the probability that a randomly chosen arrangement of the 8 letters in the word COCOONED has all three Os together given that the two Cs are next to each other.
CAIE S1 2020 November Q5
5 The 8 letters in the word RESERVED are arranged in a random order.
  1. Find the probability that the arrangement has V as the first letter and E as the last letter.
  2. Find the probability that the arrangement has both Rs together given that all three Es are together.