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 zeroarea "triangle", such as 123 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 AZ
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 20100319 10:59:55 