# Practice Paper 4 Question 1

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

## Related topics

## Hints

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