 I'm Kanika and I'm going to help you to solve the following question. The question says, if four 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? First part is that digits are repeated. Second part is the repetition of digits is not allowed. Begin with the solution, probability of forming the number divisible by 5 when the digits are repeated. Now remember, can be filled in 5 into 5 into 5 base and this is equal to 125 base. As we have to form the number with 5 digits and the repetition of digits is allowed and you should also know that as we have to form a number greater than 5,000 base can only be occupied by 5 or 7. Similarly, if is filled up with, then the base is 2nd, 3rd and 4th and we filled in 5 into 5 into 5 base that is 125 base. The number of exhaustive cases when four digit number greater than 5,000 is formed is equal to 125 plus 125 is equal to 250. Now the four digit number should be divisible by 5. Now the number will be divisible by 5. First place is filled up with either 5 or 0 and we know that first place can only be occupied by 5 or 7. Now the remaining 2nd and 3rd places are at this 35 base. So number of numbers which are divisible by 5 will be 4 into 25. The probability of forming a number greater than 5,000 and divisible by 5. When repetition of digits is allowed is 100 by 2 by forming a number greater than 5,000 and divisible by 5. When repetition of digits is not allowed, so 2nd, 3rd, 4 into 3 into 2 base that is 3, 4 base. When first place is filled up with 7, then places 7 can be filled in 4 into 3 into 2 base. So total number of cases when four digit number and repetition of digits is not allowed will be 24 plus 24 that is 48 can be filled 3 into 2 base that is 6 base. So when digits are not repeated then the number of numbers divisible by 5, 6 plus 6 plus 6 forming a number greater than 5,000 and divisible by 5. When repetition of digits is not 18 by 48 that is 3 by...