The given set is a set of all three-digit numbers and the number of numbers in the set =\(900\).
The number of three-digit numbers having no digits repeating = \(9×9×8 = 648\)
Required answer =\(900-648=252\)
The total count of integers \(= 999 - 100 + 1 = 900\)
Let \(N\) be the number of integers with no repeated digits.
Since we have \(10\) digits (\(0\) through \(9\)), and the first digit cannot be \(0\), there are \(9\) options for the first digit.
Similarly, for the second digit, there are \(9\) options, and for the third digit, there are \(8\) options.
Thus, the total count of integers with no repeated digits \(= N = 9 × 9 × 8 = 648\)
The count of integers with at least one digit repeated \( = 900 - 648 = 252\)
Therefore, there will be \(252\) integers with at least one repeated digit.
So, the answer is \(252\).
Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option from the following:
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.
Reason (R): For any two natural numbers, HCF × LCM = product of numbers.