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Question

A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. Find the probability that the number is divisible by 4.


Solution

A number divisible by $$4$$ formed using the digits $$1,2,3,4$$ and $$5$$ should have the last two digits $$12$$ or $$24$$ or $$32$$ or $$52$$.

In each of these cases, the five digits number can be formed using the remaining $$3$$ digits in $$3! = 6$$ ways.

A number divisible by $$4$$ can be formed in $$6\times 4=24$$ ways

Total number of 5-digit numbers that can be formed using the digits $$1,2,3,4$$ and $$5$$ without repetition $$=5!=120$$

Required probability $$= \dfrac{24}{120} = \dfrac{1}{5}$$


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