Exercise · ZW-MULTIPLICATION-PRINCIPLE-009 · ★★★ Advanced

Without repeating digits, how many odd 4-digit numbers (1000 to 9999) are there?

Choose one option.

Show answer

A. \(2240\)

Explanation

Choose the last digit first (5 odd digits), then the first (8: not 0 and not the one used), then 8 and 7 for the middle ones: \(5\cdot 8\cdot 8\cdot 7=2240\).

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Review the concept: Multiplication principle

If a task is done in successive steps and step \(i\) admits \(n_i\) options regardless of how the earlier steps were done, the total number of ways \(N\) is the product of those numbers.

\[N=n_1\cdot n_2\cdots n_k\]

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