Funatic Maths

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- Paper 1

Question 10

In a certain country, 1010-digit telephone numbers with the following format were introduced:
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Digits may be repeated.
10.110.1 How many possible 1010-digit telephone numbers could be formed? (2)(2)
10.210.2 Certain restrictions were placed on the groups of digits:
  • Area code: must be 33 digits and the first digit can NOT be 00 or 11
  • Exchange code: must be 33 digits and the first and second digits can NOT be 00 or 11
  • Number: must be 44 digits and the first digit MUST be a 00 or 11
10.2.1\quad 10.2.1 How many valid 1010-digit telephone numbers could be formed by applying the given restrictions? (3)(3)
10.2.2\quad 10.2.2 Determine the probability that any randomly chosen 1010-digit telephone number would be a valid phone number. (2)(2)
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