Latest TCS Aptitude Question SOLUTION: . . . . . . . . . . . . . . . Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle? a. 440/455 b. 434/455

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Here is 15 dots.
If you select 3 dots randomly, what is the probability that 3 dots make a triangle?

a. 440/455
b. 434/455
c. 449/455
d. 436/455

Asked In TCS Sanu Panji (9 years ago)

Unsolved Read Solution (15)

Is this Puzzle helpful?   (22)   (3) Submit Your Solution Probability

Read Solution (15) :

Surit Datta  (9 years ago)

total ways to select 3 points = 15C3
when it will not form a triangle = 15C3 - when it will form a line.
horizontal lines = 3*5C3
vertical lines = 5*3C3
diagonal lines = 6
probability = 414/455
It may possible that i have made some mistake in calculation.
Please correct me if so.
But I think this is an easy way to calculate it.

Is this solution Helpfull? Yes (27) | No (12)  

akshat sinha  (8 years ago)

total ways to select 3 points = 15C3
when it will not form a triangle = 15C3 - when it will form a line.

horizontal lines =(_) 3*5C3
._._._._._
._._._._._
._._._._._


vertical lines = 5*3C3
.-.-.-.-.
|||||
.-.-.-.-.
|||||
.-.-.-.-.
|||||

diagonal lines = 8
.....
/
.....
/
.....


._._._._.

._._._._.

._._._._.



._._._._.
/ / /
._._._._.
/ / /
._._._._.


probability = 412/455

Is this solution Helpfull? Yes (21) | No (8)  

Arnab Maity  (8 years ago)

I think there seem some problem with this question. Total ways of selecting 3 dots out of 15 is 15C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram. If we select any 3 dots from the red lines they may not form a triangle. They are 3 x 5C3 = 30. If we select the three letters from blue lines, they may not form a triangle. They are in total 5 ways. Also there are 6 others lines which don't form a triangle. Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43. So we can form a triangle in 455 - 43 = 412. So answer could be 412/455.

Is this solution Helpfull? Yes (11) | No (15)  

Pravir Karna  (9 years ago)

It shud be 438/455

Is this solution Helpfull? Yes (8) | No (14)  

akshat sinha  (8 years ago)

Check answer from here:- http://linkshrink.net/7lr4nE
From above link you can conclude why the answer could be 412.
Happy reading :)

Is this solution Helpfull? Yes (4) | No (6)  

sanit kumar kundu  (8 years ago)

correct ans is 414/455

Is this solution Helpfull? Yes (2) | No (5)  

sachin chaturvedi  (9 years ago)

1 > 440/455

Is this solution Helpfull? Yes (1) | No (10)  

SUPRIYA SAWARN  (8 years ago)

total selection of 3 points to form triangle out of 15 points=15C3=455
now we have to substract the collinear points which can form a line.
horizontal lines of selection=5C3=10 and dis can be done in 3 ways so total horizontal lines=3*10=30.
now vertical lines=5*3C3=5.
total diagonals which can form a line=6.
so total number of line=30+5+6=41
total triangles=455-41=414
hence probability=414455

Is this solution Helpfull? Yes (1) | No (6)  

akshat sinha  (8 years ago)

Please see link,http://linkshrink.net/7lr4nE
the m4maths, reduce spaces, which make answer not understandable.

Is this solution Helpfull? Yes (1) | No (3)  

SheelaP  (9 years ago)

give detail explaination

Is this solution Helpfull? Yes | No (4)  

san gohan  (9 years ago)

i guess option d

Is this solution Helpfull? Yes | No (6)  

kishore  (9 years ago)

i dont know the question exactly .what is the answer that is related to base 10 asked in tcs 2015.
ans options is a. 364 or b.436

Is this solution Helpfull? Yes | No (3)  

Brajeshrai  (9 years ago)

Ans is b
No of horizontal triangle+no of vertical triangle-common triangle
300+140-4=436/455

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sudha chandu  (8 years ago)

please give the correct answer...

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Murtaza  (6 years ago)

Though the answer is 414/455. But the real question here is, how the **** am I going to select an option that is not available. Well done TCS. Kudos.....

Is this solution Helpfull? Yes | No (1)  

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