Manipal Entrance Test 2015 Math Paper

Number of ways of selecting three numbers one on each card =100×100×100=1003
We know that (2n+1),(2n2+2n) and (2n2+2n+1) are Pythagorean triplets.
∴ For n=1,2,3,4,5,6, we get the lengths of three sides of a right angled triangle such that its hypotenuse is less than or equal to 100‌cm.
Now, one Pythagorean triplet (e.g. 3, 4, 5; 5, 12, 13; etc.) can be chosen in 3! ways.
therefore Number of ways of selecting 6 Pythagorean triplets =6×3!
Hence, required probability =

6×3!

1003