The number of positive integers which can be formed by any number of digits from $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ but using each digit not more than once in each number are

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The number of positive integers which  can be formed by any number of digits from $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ but using each  digit not more than once in each number are

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One digit  numbers                                $$=$$     −→$$5$$      $$($$ except $$0)$$ Two digited numbers                                 $$=$$    −−→$$5$$·$$5=25$$   $$($$ first blank can be filled in $$5$$ ways (except$$ $$0) and the second blank can be                                                                                                                                                                                                filled in $$P(5$$,$$1)$$ $$ways)$$.  Three digited numbers                             $$=$$     −−−→$$5$$×$$P2$$   $$5=100$$ $$($$ first blank can be filled in $$5$$ ways and the remaining $$2$$ blanks can be                                                                                                                  filled in $$P(5$$,$$2)$$ ways.  $$)$$   Four digited numbers                              $$=$$    −−−−→$$5$$.$$P3$$   $$5=300$$   Five digited numbers                               $$=$$   −−−−−→$$5$$.$$P4$$   $$5=600$$   Six digited numbers                                 $$=$$    −−−−−−→$$5.5$$!$$=600$$     Number of ways                                      $$=1630$$

The number of positive integers which can be formed by any number of digits from 0, 1, 2, 3, 4, 5 but using each digit not more than once in each number are

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