How many three-digit numbers are there, with distinct digits, wit… - Vidyadip

Question

How many three-digit numbers are there, with distinct digits, with each digit odd?

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Answer

The odd number digits are 1, 3, 5, 6, 9 Total number of odd digits = 5 $\therefore$ Required number of 3 digit num bars = number of arrangenments of 5 digits by taking 3 at a time $=\ ^{5}\text{P}_3$$=\frac{5!}{(5-3)!}$
$=\frac{5!}{2!}$
$=\frac{5\times4\times3\times2!}{2!}$
$=60$
Hence, total number of 3 digit numbers are 60.

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