Choose the correct answer out of four given options in each of the exercise without repetition of the numbers, four digit numbers are formed with the numbers 0,2,3,5 . The probability of such a number divisible by 5 is
A. \frac{1}{5}
B. \frac{4}{5}
C. \frac{1}{30}
D. \frac{5}{9}
Choose the correct answer out of four given options in each of the exercise without repetition of the numbers, four digit numbers are formed with the numbers 0,2,3,5 . The probability of such a number divisible by 5 is
A. \frac{1}{5}
B. \frac{4}{5}
C. \frac{1}{30}
D. \frac{5}{9}

Solution:

Option (D) 5 / 9
Explanation:
The digits 0,2,3,5 we have.
It is known that, if unit place digit is { }^{\prime} 0^{\prime} or { }^{\prime} 5^{\prime} then the no. is divisible by 5
If the unit place is { }^{\prime} 0^{\prime}
Then we can fill the first three places in 3 ! ways =3 \times 2 \times 1 \times 1=6
If the unit place is ‘ 5^{\prime}
Then we can fill the first place in 2 ways and fill the second and third place in 2 ! ways =2 \times 2 \times 1 \times 1=4
\therefore Total no. of ways =6+4=10=\mathrm{n}(\mathrm{E})
Total no. of ways of arranging the digits 0,2,3,5 to form 4 – digit no. without repetition is 3 \times 3 \times 2 \times 1=18
Probability =\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}

\therefore The required probability =\frac{10}{18}=\frac{5}{9}
As a result, the correct option is (D).