How many three digits numbers less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ when the digits are not repeated?

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Solution

$¯ ¯ ¯ 4 ¯ ¯ ¯ 5 ¯ ¯ ¯ 6$

Unit's place - 6 ways.
Ten's place -5 ways.
Hundredth's place - 4 ways.

Total no. of digital possible $= 6 \times 5 \times 4$
$= 120$

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