OCR S1 2006 June — Question 3

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2006
SessionJune
TopicPermutations & Arrangements
TypeArrangements with adjacency requirements

3 Each of the 7 letters in the word DIVIDED is printed on a separate card. The cards are arranged in a row.
  1. How many different arrangements of the letters are possible?
  2. In how many of these arrangements are all three Ds together? The 7 cards are now shuffled and 2 cards are selected at random, without replacement.
  3. Find the probability that at least one of these 2 cards has D printed on it.