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Question
How many three-digit numbers are there, with distinct digits, with each digit odd?
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Solution
The odd digits are 1, 3, 5, 7 and 9.
Required number of ways = Number of arrangements of five digits ( 1, 3, 5, 7 and 9), taken three at a time = 5P3
\[ = \frac{5!}{2!}\]
\[ = \frac{5 \times 4 \times 3 \times 2!}{2!}\]
\[ = 5 \times 4 \times 3\]
\[ = 60\]
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