Without repetition of the numbers,
Question:

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:

D. 5/9

Explanation:

We have digits $0,2,3,5$.

We know that, if unit place digit is ‘ 0 ‘ or ‘ 5 ‘ then the number is divisible by 5 If unit place is ‘ 0 ‘

Then first three places can be filled in $3 !$ ways $=3 \times 2 \times 1 \times 1=6$ If unit place is ‘ 5 ‘

Then first place can be filled in two ways and second and third place can be filled in $2 !$ ways $=2 \times 2 \times 1 \times 1=4$

$\therefore$ Total number of ways $=6+4=10=\mathrm{n}(\mathrm{E})$

Total number of ways of arranging the digits $0,2,3,5$ to form 4 – digit

numbers without repetition is $3 \times 3 \times 2 \times 1=18$

Probability $=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}$

$\therefore$ Required probability $=\frac{10}{18}=\frac{5}{9}$

Hence, the correct option is (D).