There are $$720$$ permutations of the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$. Suppose these permutations are arranged from smallest to largest numerical values, beginning from $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ and ending with $$6$$ $$5$$ $$4$$ $$3$$ $$2$$ $$1$$ Then the digit in unit place of number at $$267Tth$$ position is $$________$$ .

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Infinity Learn · Accepted Answer

Number of numbers beginning with $$1=120$$                                                                  Number of numbers beginning with $$2=120$$                                                                 Starting with $$31$$ ………………………………$$=24Starting$$ with $$3214$$ …………………………….$$=2Finally$$                                                               $$=$$ $$1$$                                                                                                                                             Hence, unit place digit of $$267th$$ number is $$6$$.

There are 720 permutations of the digits 1, 2, 3, 4, 5, 6. Suppose these permutations are arranged from smallest to largest numerical values, beginning from 1 2 3 4 5 6 and ending with 6 5 4 3 2 1 Then the digit in unit place of number at 267Tth position is ________ .

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