CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This is a delighful question that is based on Number Systems. Anyone who has gone through 2IIM's CAT Blueprint , would know that Number Theory is the building block of the CAT Syllabus because it is entirely based on simple Mathematics and trains you to develop a sense of numbers. Give this question a try and have a look at the video solution to cross-check your answer.

Question 14 : How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that in every such number, each digit is used at most once and the digits appear in the ascending order? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Number Theory

Let us consider the case of 2-digit numbers
2 numbers can be chosen from the given set by ⁹C₂ ways. There is only one way of arranging them in ascending order.
Similarly, the remaining numbers can be chosen and arranged in ascending order by ⁹C₂+⁹C₃+......+⁹C₈+⁹C₉ ways
We know, ⁿC₀+ⁿC₁+.....+ⁿC_n-1+ⁿC_n = 2ⁿ
So, the total number of ways = 2⁹ – ⁹C₀ – ⁹C₁
512-10 = 502

The question is "How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that in every such number, each digit is used at most once and the digits appear in the ascending order?"

Hence, the answer is 502 units.