CAIE S1 2014 June — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicPermutations & Arrangements
TypeDigit arrangements forming numbers

7 Nine cards are numbered \(1,2,2,3,3,4,6,6,6\).
  1. All nine cards are placed in a line, making a 9-digit number. Find how many different 9-digit numbers can be made in this way
    (a) if the even digits are all together,
    (b) if the first and last digits are both odd.
  2. Three of the nine cards are chosen and placed in a line, making a 3-digit number. Find how many different numbers can be made in this way
    (a) if there are no repeated digits,
    (b) if the number is between 200 and 300 .