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Question

How many five digits numbers can be formed using the digits 0,1,2,3 and 5 which are divisible by 5 without repetition of the digits?

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Solution

When the unit digit of a number is either 0 or 5 then the whole number is divisible by 5

(i) when unit digit of a number is 5 then,

The number of five digited numbers can be formed by using the digits 0,1,2,3,5 without repetition of the digits =(3)(3)(2)(1)=18

(ii) when unit digit of a number is 0 then,

The number of five digited numbers can be formed by using the digits 0,1,2,3,5 without repetition of the digits =(4)(3)(2)(1)=24

Total numbers =18+24=42 (Ans)

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