If a number is chosen at random from out of the four digited numbers formed by using the digits $0,1,2,3,4,6$ without repetition, then the probability that it is divisible by 4 , is

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Aicharya · Accepted Answer

If the number divisible by 4 using digits 0,1 , $2,3,4,6$ unit place digit is even. Case I. If unit digit is 0 , then tens place possible digits is $2,4,6$

Possible outcome $=4 \times 3 \times 3=36$ Case II. If unit digit is 2 , then tens place digits are 1 and 3 Possible outcomes $ =3 \times 3 \times 2=18 $

Case III. If unit digit is 4 , then tens digits are 0,2 and 6 . (a) If tens digit 0 Possible ways $ =4 \times 3=12 $ (b) If tens digit not zero, i.e. (2 and 6) Possible ways $ =3 \times 3 \times 2=18 $

So, required ways, if unit digit is $4=18+12=30$. Case IV. If unit digit is 6 , then digit are 1 and 3 Possible ways

Hence, total number of number which is divisible by $4=36+18+30+18$ $=102$ Now, total number of ways of form four digit number using $0,1,2,3,4,6$ is

Total number of 4 digit number $ \begin{array}{r} =5 \times 5 \times 4 \times 3=300 \\ \therefore \text { Required probability }=\frac{102}{300}=\frac{17}{50} \end{array} $

If a number is chosen at random from out of the four digited numbers formed by using the digits $0,1,2,3,4…

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