How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?
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Total number of numbers from 100 to 999 = 900 The number of three digits numbers with unique digits: _ _ _ The hundredth's place can be filled in 9 ways ( Number 0 cannot be selected) Ten's place can be filled in 9 ways One's place can be filled in 8 ways Total number of numbers = 9*9*8 = 648 Number of integers in the set {100, 101, 102, ..., 999} have at least one digit repeated = 900 - 648 = 252 View Video SolutionQuestion Description Solutions for How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Here you can find the meaning of How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer?, a detailed solution for How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer? has been provided alongside types of How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?Correct answer is '252'. Can you explain this answer? tests, examples and also practice CAT tests. This question is from Permutation and Combination. From a set of integers, we need to find the numbers of integers that have at least one digit repeated. CAT Permutation and Combination and Probability is an important topic in the CAT Exam. A range of questions can be formed from this topic. In CAT Exam, one can generally expect to get 2~3 questions from these topics. Question 16 : How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated? Correct Answer: 252 🎉 Fabulous 4,000 off on CAT '23 courses Valid until 1st Nov2IIM : Best Online CAT Coaching.Video Explanation
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| a | b | c | |
| Possibilities | 1 to 9 | 0 to 9 except a | 0 to 9 except a and b |
| Number of Possibilities | 9 | 9 | 8 |
The number of integers that between 100 and 999, which do not have repetitions = 9 × 9 × 8
Therefore, the number of integers that have repetitions = 900 - 9 × 9 × 8
= 9 (100 - 9 × 8)
= 9 (28)
= 180 + 72 = 200 + 52 = 252
The question is "How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?
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