Numbers 1,2,3, , 100 are written down on each of the cards A, B and C . One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm) of three sides of a right angled triangle, is

Step-by-step solution

Number of ways of selecting three numbers one on each card =100 100 100=100^3 We know that (2 n+1), (2 n^2+2 n ) and (2 n^2+2 n+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 100 cm . Now, one Pythagorean triplet (e.g. 3, 4, 5; 5, 12, 13; etc.) can be chosen in 3! ways. Number of ways of selecting 6 Pythagorean triplets =6 3 ! Hence, required probability = 6 3! 100^3