OCR S1 2012 January — Question 9

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2012
SessionJanuary
TopicPermutations & Arrangements
TypeDigit arrangements forming numbers

9 A bag contains 9 discs numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 .
  1. Andrea chooses 4 discs at random, without replacement, and places them in a row.
    (a) How many different 4 -digit numbers can be made?
    (b) How many different odd 4-digit numbers can be made?
  2. Andrea's 4 discs are put back in the bag. Martin then chooses 4 discs at random, without replacement. Find the probability that
    (a) the 4 digits include at least 3 odd digits,
    (b) the 4 digits add up to 28 .