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  4. The number of positive integers less than 40,000 that can be formed by using all the digits 1, 2, 3, 4 and 5 is equal to

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Q. The number of positive integers less than $40,000$ that can be formed by using all the digits $1, 2, 3, 4$ and $5$ is equal to

KEAMKEAM 2010Permutations and Combinations

Solution:

$ \underset{3}{\mathop{\square }}\,\,\,\,\underset{4}{\mathop{\square }}\,\,\,\,\underset{3}{\mathop{\square }}\,\,\,\,\underset{2}{\mathop{\square }}\,\,\,\,\underset{1}{\mathop{\square }}\,\underset{(ways\text{ }to\text{ }filling\text{ }the\text{ }box)}{\mathop{{}}}\, $
$ \therefore $ Required number of positive integer
$=3\times 4\times 3\times 2\times 1 $
$=72 $