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. $\frac{5}{9}$

Home » 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 The probability of such a number divisible by 5 is A. B. C. D.

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. $\frac{5}{9}$

CBSE | Class 11 | Maths | NCERT Exemplar | Probability

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 $=\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }}$