1. 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. 438/455.

• ANS)Dummy question...really answer is 412/455
• 9 years agoHelpfull: Yes(8) No(2)
• sol:
  The no of ways to select dots is: 15c3=455.
  The no. of ways not to get a triangle= 15.
  therefore probability will be: 455-15/455
  I.e: 440/455.
• 9 years agoHelpfull: Yes(6) No(0)
• Guys this is simple if they had provided us the diagram, frst f all, evaluate all the three points that cannt from an triangle 🔺. Only possible if they are linear right.
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  Take x axis, nw choose 3 dots from one row 5c3,tht is 10,for three rows 30.
  Take y axis, 3 dots in each column, so 5 ways its forming an linear line nt triangle,
  Now two points will line through the centre point from the both corner of the square shaped dots,total 2 ways, done,
  Now, 1st dot of 1st row with 2nd dot of second row and 3rd dot of third rows are one linear points, if we pen through, 3 ways towards right and 3 ways towards left, total 6 ways, and now sum up the impossible points that cannt form the triangle =30+5+2+3+3=43,,,455-43=412,,so,412/total possibility
• 9 years agoHelpfull: Yes(5) No(1)
• I'm assuming that's three distinct dots. If they don't form a triangle, then they're collinear. Let's enumerate the collinear cases.
  
  They could be three dots in one row (forming a horizontal line). There are (5c3)=10 ways of selecting three dots from a row, and there are three rows, so that makes 30 cases.
  
  They could be (the) three dots in a column, and there are five columns, so that makes 5 cases.
  
  They could be three dots in positions (1,i),(2,i+1),(3,i+2), i∈{1,2,3} (thus forming a diagonal of some sort). There are three cases of this kind. But they could also form a diagonal slanted in the opposite direction, so there are three more cases, making a total of 6 cases.
  
  They could be a diagonal of the form (1,1),(2,3),(3,5), or the one in the opposite direction, so that makes 2 cases.
  
  Thus, there are totally 43 cases. The total number of ways of selecting three dots from the matrix is (153)=455. Thus, there are 455−43=412 ways of selecting three dots that form a triangle. The probability is, therefore,
  
  412/455.
• 9 years agoHelpfull: Yes(4) No(2)
• ANS:)- 440/455 is the ri8 answer.
  
• 9 years agoHelpfull: Yes(3) No(2)
• please explain this....!!!
• 9 years agoHelpfull: Yes(1) No(0)
• option of this question is wrong
  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.
• 9 years agoHelpfull: Yes(1) No(2)
• 3*5c3+5+6+2=43/455
  1-43/455=412/455
• 9 years agoHelpfull: Yes(0) No(4)
• plz send me in my mail id -rrdaisykumari1@gmail.com
  
• 9 years agoHelpfull: Yes(0) No(0)
• plz expln in detail
  
• 9 years agoHelpfull: Yes(0) No(0)
• This is dummy question and Final ans is 412/455
• 9 years agoHelpfull: Yes(0) No(0)
• . . . . .
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  by this 15dots first you have to find how many lines are there that are not form a triangle i.e 30+6+5+2 = 43
  now total ways of selecting 3 dots out of 15 i.e 15c3 = 455
  3 dots make triangle = 455-43 = 412
  ans is 412/455
• 5 years agoHelpfull: Yes(0) No(0)