Multiple choice

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

  1. $\dfrac{4}{100^3}$
  2. $\dfrac{3}{50^3}$
  3. $\dfrac{3!}{100^3}$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A right triangle requires a^2 + b^2 = c^2. For numbers 1-100, the number of such triples is small (e.g., 3-4-5, 6-8-10, etc.). The total outcomes are 100^3. The count of valid triples is much higher than the options provided, making 'None of these' the correct choice.

AI explanation

Applying the multiplication rule for independent events, the total number of possible ways to select three numbers from 1 to 100 is 100^3. To form a right-angled triangle, the selected numbers must represent a Pythagorean triple, and for a generic right triangle, there are only a few valid sets like (3, 4, 5), (6, 8, 10), and (5, 12, 13) that appear within this range. The exact number of favorable permutations, such as 3! for multiples of (3, 4, 5) and 3! for (5, 12, 13) and its multiples, does not match any of the simple expressions provided in the options. The result is None of these.

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