# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | Number theory Questions | Question 14

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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##### 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+.....+nCn-1+nCn = 2n
So, the total number of ways = 299C09C1
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.

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