The figures $$4$$,$$5$$, $$6$$, $$7$$,$$8$$ are written in every possible order. The number of numbers greater than $$56000$$ is

Question

Infinity Learn · Accepted Answer

The number forms by the figure $$4$$, $$5$$, $$6$$, $$7$$, $$8$$ which is greater than $$56000$$ is in two cases.Case I: Let the ten thousand digit place number be greater than $$5$$.The number of numbers $$=3C1$$×$$4C1$$×$$3C1$$×$$2C1$$×$$1C1=3$$×$$4$$×$$3$$×$$2$$×$$1=72Case$$ ll: Let the ten thousand digit number be $$6$$ and thousand digit number be either $$6$$ or greater than $$6$$.Then, the number of numbers $$=3C1$$×$$3C1$$×$$2C1$$×$$1C1=3$$×$$3$$×$$2$$×$$1=18$$ Required number of ways $$=$$ $$72$$ $$+$$ $$18$$ $$=$$ $$90$$

The figures 4,5, 6, 7,8 are written in every possible order. The number of numbers greater than 56000 is

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