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# 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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