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The Computer Laboratory

Practice Paper 4 Question 1

How many \(10\) digit natural numbers do not contain the digit \(6?\) Numbers cannot start with zero.

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Hints

  • Hint 1
    How many values can the first digit take?
  • Hint 2
    For each of those values, how many different numbers that do not contain the digit \(6?\)
  • Hint 3
    Think of the different values each of the remaining digit can take.

Solution

The first digit can be 8 different options \((\)i.e. not \(0\) and \(6)\) and the rest can be anything but \(6.\) The number of numbers without any 6s is \(8 \times 9^9.\) (Note: We don't expect you to calculate the final value!)

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