The sum of all the numbers that can be formed with the digits $$2$$, $$3$$, $$4$$, $$5$$ taken all at a time is

Question

Infinity Learn · Accepted Answer

The total number of numbers that can be formed with the digits $$2$$, $$3$$, $$4$$, $$5$$ taken all at a time $$=4P4=4$$!$$=24$$. Consider the digit in the unit’s place in all these numbers. Each of the digits $$2$$, $$3$$, $$4$$, $$5$$ occurs in $$3$$! $$=$$ $$6$$ times in the unit’s place∴ total for the digits in the unit’s place $$=$$ (2$$ $$+$$ $$3$$ $$+$$ $$4$$ $$+$$ $$5) $$6$$ $$=$$ $$84Since$$ each of the digits $$2$$, $$3$$, $$4$$, $$5$$ occurs $$6$$ times in any one of the remaining places∴ the required total $$=$$ $$84$$ (1$$ $$+$$ $$10$$ $$+$$ $$102$$ $$+$$ $$103) $$=$$ $$84$$ (1111) $$=$$ $$93324$$.

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is

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