The number of even numbers greater than $$100$$ that can be formed by the digits $$0$$, $$1$$, $$2$$, $$3$$ (no$$ digit being $$repeated) is

Question

Infinity Learn · Accepted Answer

The numbers are of three or four digits.To find the number of even numbers of three digits—The unit’s place must be filled by $$0$$ or $$2$$.∴ The number of even numbers of three digits (having$$ or not having $$0$$ in hundred’s $$place) $$=2P1$$×$$3P2$$.But the number of even numbers of three digits having $$0$$ in hundred’s place $$=2P1$$ $$($$∵ unit’s place is naturally filled by $$2$$ and ten’s place by one of $$1$$ and $$3)$$.∴ The number of even numbers of three $$digits=2P1$$×$$3P2$$−$$2P1$$            (1)Similarly$$, the number of even numbers of four $$digits=2P1$$×$$3P3$$−$$2P2$$            $$(2)Adding$$ $$(1) and (2), we get the number of even numbers greater than $$100=$$ $$2P1$$×$$3P2$$−$$2P1+$$ $$2P1$$×$$3P3$$−$$2P2=2$$×$$3$$×$$2$$−$$2+2$$×$$3$$×$$2$$×$$1$$−$$2$$×$$1=20$$

The number of even numbers greater than 100 that can be formed by the digits 0, 1, 2, 3 (no digit being repeated) is

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