Use permutations and combinations to compute probabilities of compound events and solve problems.
Count possible outcomes with restrictions using the multiplication principle, factorials, or combinations
Problem
Count \(9\) nonzero choices for the first digit, then \(9\), \(8\), and \(7\) remaining choices for the later positions.
Big Picture
What this problem is really about
Restrictions can make different positions have different numbers of available digits. We’ll handle the nonzero first position first, restore zero to the pool for later positions, decrease the count after each used digit, and multiply the stage counts without treating the positions as interchangeable.
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