# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Permutation and Combination Questions | Question 29

Permutation and Combination is a crucial topic in the CAT exam. This question talks about five diameters of a circle, but it has a flavor of permutation and combination hidden inside it. Will you be able to find that out? Give this question a shot and then watch how Rajesh has solved it.

Question 29 : Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle? [TITA]

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### Explanatory Answer

##### Method of solving this CAT Question from Permutation and Combination

Given that AB , CD , EF , GH and JK be five diameters of a circle with center at O.
We have to find by how many ways three points can be chosen out of A , B , C , D , E , F , G , H , J , K and O so as to form a triangle.
We know that any three points lying on the circle are non collinear.
There are 11 points here we have to choose from any three points that are not collinear.
From these 10 points A, B, C, D, E, F, G, H, J, K we can select any three points on the circle such that they are non collinear. We can take O and then from remaining 10 we can take remaining two.
Since AOB , COD , GOH , EOF , JOK cannot form triangles, 5 can be subtracted.
10C3 + 10C2 - 5 = $$frac{10 × 9 × 8}{1 × 2 × 3}$ + $\frac{10 × 9}{1 × 2}$ - 5 ⟹ 120 + 45 – 5 = 160 ways. The question is "Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle? [TITA]" ##### Hence, the answer is 160 ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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