Latest Elitmus Aptitude Question SOLUTION: 4*4 matrix find probability of creating a triangle with the help of 3 points

• Placement Papers
• /
• Elitmus

Elitmus Question Papers:

(#M40019221) ELITMUS question quant Keep an EYE

4*4 matrix find probability of creating a triangle with the help of 3 points

Asked In Elitmus Krishanu chatterjee (10 years ago)

Unsolved Read Solution (22)

Is this Puzzle helpful?   (6)   (0) Submit Your Solution

Read Solution (22) :

PREM KUMAR  (10 years ago)

129/140
Explanation:

total outcome=16c3
unfavorable outcome:
if we select
all three point from a row = 4c3*4!/3!=16;
all three point from a col = 4c3*4!/3!=16;
all thee point from on diognal=2*(3c3+4c3+3c3)=12;
so total unfavorable outcome=44;
so the required probabilty=1-44/560=129/140;

Is this solution Helpfull? Yes (14) | No (5)  

Anubhav Guleria  (10 years ago)

13/14
Explanation:
p(create a triangle)= 1 - p(triangle never formed)
=1 - (10*4C3)/16C3 [10= 4 rows 4 cols and 2 diagonals]

Is this solution Helpfull? Yes (8) | No (5)  

TEJ PRAKASH TEWARI  (10 years ago)

129/140
Explanation:
Probability unfavorable outcomes=10*4C3/16C3+4*3C3/16C3
[4 rows 4cols 2 diagonals having 4 points in same line(i.e 4+4+2=10) and 4 diagonals having only 3 points in same line]
(10*4+4)/16C3=4*11*3*2/(16*15*14)=11/140
So Probability of favorable outcomes=1-11/140=129/140

Is this solution Helpfull? Yes (7) | No (1)  

Roshan jha  (10 years ago)

ans is 129/140
collinear 4 points=10 (4 row 4col 2 diag)
collinear only 3 points=4 (diagonolly)
so no. of tritangle form= 16c3-10x4c3-4x3c1=516
prob=516/560= 129/140

Is this solution Helpfull? Yes (3) | No   

Krishanu chatterjee  (10 years ago)

the only way there will be no triangles formed when u select all 3 points in the same line forming a straight line that is by 4c3 in each row or column so total ways by which these st lines be formed is by 4c3*8=32
so 16c3-32=528
so probability of forming triangle is 528/560

Is this solution Helpfull? Yes (2) | No (3)  

Abdul Hadee  (9 years ago)

yup u r right... total ways of forming a line using three points is
4* 4C3 (rows) //(4 rows if selecting 3 point from each row)
+ 4*4C3 (columns) //(4 rows if selecting 3 point from each column )
+ 2*4C3 (diagonals) //(2 diagonals having 4 point selecting 3 from it)
+ 4 (shorter diagonals) //(matrix begin with (1,1) then first diagonal (1.2)(2,3)(3,4)
second (1,3)(2,2) (3,1) third (2,1)(3,2)(4,3) fourth (2,4)(3,3)(4,2)
= 44
Thus 1 - (44/560) will be the ans 129/140

Is this solution Helpfull? Yes (2) | No   

shekhar pankaj  (10 years ago)

Probality???? Is there any unsure event there???

Is this solution Helpfull? Yes (1) | No   

shailesh  (10 years ago)

=1-24/560
=536/560
=67/70

Is this solution Helpfull? Yes (1) | No (2)  

shailesh  (10 years ago)

@ anubhav u forget that at above the diagonal and below the diagonal their are 3 points in diagonally make a fig. and notice that
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

3 6 9 are also 3 points that make no triangle

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

kanaka shrikanth  (10 years ago)

please mention the question correctly ....

Is this solution Helpfull? Yes | No   

suryakant kumar  (10 years ago)

there is points 4x4 (i.e 16 points) find the total number of triangle form using 3 points of this 4x4 points.

Is this solution Helpfull? Yes | No   

Sumit  (10 years ago)

16!/13!*3!

Is this solution Helpfull? Yes | No (4)  

SAMBIT KUMAR GHOSH  (10 years ago)

please explain this question clearly...

Is this solution Helpfull? Yes | No   

Krishanu chatterjee  (10 years ago)

its probability>> 4*4 matrix where there is 16 points 3 points can be selected thats is 16c3=560 ways ok now tell me the probability among this how many will form a triangle (means selecting 3 points out of 16 whts is probability)..............will be telling ur ans shortly

Is this solution Helpfull? Yes | No   

SAMBIT KUMAR GHOSH  (10 years ago)

guys any1 can give me an ideal soln of this sum...if yes...pls give !!!

Is this solution Helpfull? Yes | No   

SAMBIT KUMAR GHOSH  (10 years ago)

thanks krishanu !!!

Is this solution Helpfull? Yes | No   

SAMBIT KUMAR GHOSH  (10 years ago)

so the ultimate ans is 33/35

Is this solution Helpfull? Yes | No (4)  

shubham kesarwani  (10 years ago)

please anyone explain the right answer.

Is this solution Helpfull? Yes | No   

zen mano  (10 years ago)

132/560 = 33/140

Is this solution Helpfull? Yes | No   

shubham kesarwani  (10 years ago)

sambit can u plz explain how you solved it.

Is this solution Helpfull? Yes | No   

deepak srivastava  (10 years ago)

1- (10*4c3 - 4)/16c3

Is this solution Helpfull? Yes | No   

sudhakar verma  (10 years ago)

the ans of @roshan jha and @prem kumar is right. i.e. 129/140 . rest all are wrong.
plz correct them.
:)

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.