If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?
If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?
When the digits are repeated
since four - digit numbers greater than $5000$ are formed, the leftmost digit is either $7$ or $5 .$
The remaining $3$ places can be filled by any of the digits $0,\,1,\,3,\,5,$ or $7$ as repetition of digits is allowed.
$\therefore$ Total number of $4\, -$ digit numbers greater than $5000=2 \times 5 \times 5 \times 5-1$
$=250-1=249$
$[$ In this case, $5000$ can not be counted; so $1 $ is subtracted $]$
A number is divisible by $5$ if the digit at its units place is either $0$ or $5$.
$\therefore$ Total number of $4 \,-$ digit numbers greater than $5000$ that are divisible by $5=$ $2 \times 5 \times 5 \times 2-1=100-1=99$
Thus, the probability of forming a number divisible by $5$ when the digits are repeated is $=$ $\frac{99}{249}=\frac{33}{83}$
Similar Questions
Five digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$ and $8$. What is the probability that they have even digits at both the ends
Five digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$ and $8$. What is the probability that they have even digits at both the ends
An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is
An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is
- [IIT 1993]
In a box there are $2$ red, $3$ black and $4$ white balls. Out of these three balls are drawn together. The probability of these being of same colour is
In a box there are $2$ red, $3$ black and $4$ white balls. Out of these three balls are drawn together. The probability of these being of same colour is
If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee
If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no man ?