How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?
I couldn't understand what actually the question means. Does it talk about the numbers like $222$, $999$?
2026-03-30 12:35:03.1774874103
How many numbers are there between $100$ and $1000$ such that every digit is either $2$ or $9$?
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You have three digits. Each digit must be selected from the set $\{2,9\}$. You may select either of those two for each digit. So, the first digit has two choices. The second digit has two choices. The third digit has two choices. Each choice is independent of the previous choices. This allows you to apply the product principle.
There are $2\cdot 2\cdot 2=8$ such numbers:
222, 229, 292, 299, 922, 929, 992, 999