I simultaneously toss three standard dice.
I get 3 numbers, 1 to 6, not necessarily distinct. Evaluate the probability that these numbers can represent sides of a triangle.

(In reply to re(3): Solution by Ady TZIDON)

I agree that using combinations rather than permutations results in a meaningless answer.

The only possible ambiguity would be whether a zero-area "triangle", such as 1-2-3 is permissible to count.

Modifying the simulation program to account for equality between the sum of the two smaller sides and the largest side:

DEFDBL A-Z
FOR trial = 1 TO 1000000
 a = INT(RND(1) * 6 + 1)
 b = INT(RND(1) * 6 + 1)
 c = INT(RND(1) * 6 + 1)
 IF b < a THEN SWAP a, b
 IF c < b THEN SWAP b, c
 IF b < a THEN SWAP a, b
 IF a + b >= c THEN hit = hit + 1
 tot = tot + 1
 PRINT hit; tot, hit / tot
NEXT

gives a probability of about 72.25 %, and has no relation to using combinations rather than permutations.

Posted by Charlie on 2010-03-19 10:59:55