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