Latest Elitmus Aptitude Question SOLUTION: In 4*4 matrix what is probability of forming a triangle when any three points are chosen at random? Ans. 516/560

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(#M40037100) ELITMUS Numerical Ability question Number system Keep an EYE

In 4*4 matrix what is probability of forming a triangle when any three points are chosen at random?

Ans. 516/560

Asked In Elitmus Rahul kumar (10 years ago)

Solved RAKESH Read Solution (10)

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Read Solution (10) :

RAKESH  (10 years ago)

to form a triange, we need 3 points

n(S)= 16c3 = 560

from 3 collinear point, we can't form a triangle,
no. of such combination = 4*4c3 + 4*4c3 + 2*4c3 + 4 = 44
[these are for same rows,columns,diagonals & oppisite to diagonals]

n(E)= triangle formation = 16c3 - 44 = 560-44 = 516

probability of forming a triangle = p = n(E)/n(S) = 516/560.


is it right????

Is this solution Helpfull? Yes (111) | No (9)  

raushan kumar  (10 years ago)

512/560
During the selection of three point selecting the tthree collinear piont then for each point we draw the three line the number of line is 16*3 = 48, 560-48= 512

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vishal  (10 years ago)

the opposite OF DIAgonals means the three collinear points on both sides of diagonals parallel to diagonal,and there are 2 diagonals means 2 more collinear points of line.

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Ramesh Babu  (10 years ago)

P(S) = 16c3 = 560
no.of. chances for selecting 3 points which are on the same line
= 4*4c3 + 4*4c3 + 2*4c3 + 4*3c3 = 52
(columns)+(rows)+(diagonals)+(beside diagonals 3 dots in diagonal shape)
P(E) = 560 - 52 = 508

Probability = 508/560

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

karan kapoor  (10 years ago)

@rakesh : please explain the +4 in the end of your solution

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krishna  (7 years ago)

[Ramesh Babu]
P(S) = 16c3 = 560
no.of. chances for selecting 3 points which are on the same line
= 4*4c3 + 4*4c3 + 2*4c3 + 4*3c3 = 44
(columns)+(rows)+(diagonals)+(beside diagonals 3 dots in diagonal shape- something like / and )
P(E) = 560 - 52 = 508

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Ishan  (10 years ago)

@Rakesh opposite to diagonals means?

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Diya  (10 years ago)

common no.'s are those that will give remainder of 2 when divided by 5 or 7....they will be repeated each time.

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ajay kumar roshan  (9 years ago)

sorry to inform you guys that if the 4* 4 matrice is here then the no of points in one line will be 5 and there will be 5 lines so the no of total ponits are 25.
And the ans will be:-9/46
am i right friends?

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pallavi varshney  (8 years ago)

first of all make it sure there are 25 points as there are 5*5 lines required to make 4*4 matrix....
total ways of selecting 3 points =5c3=2300
now the no of combinations of getting 3 or more collinear points= 5*5c3 (rows) + 5*5c3(columns)+2*5c3(diagonals)+2*4c3(for 45degree line formed above and below principal diagonal)+2*4c3(for 45 degree lines formed below and above other diagonal) +2*2*3c3(for 45 degree line formed above and below two diagonals formed )= 140

so ans=(2300-140)/2300=2160/2300=108/115

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