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
=