Well, it turns out that there are 243 combos that yield a tie AND the odds are also 1 in 243. This is not generally the case in all probability calculations-- it just happens to be the case because of the particular nature of this problem.
There's a couple of ways you can calculate the probability in this case. One way is the 'brute force' counting approach, which looks like this:
Total number of ways that 5 straight "ties" can happen 243 1
------------------------------------------------------ = --------- = ---
Total number of different outcomes for a 5-throw game 243 x 243 243
Alternatively, in a case where we are trying to determing the odds of a particular outcome in a series of independent events, the odds can be comuputed as Doug did: by multiplying the odds of each of the 5 independent events:
1 1 1 1 1 1
--- x --- x --- x --- x --- = ---
3 3 3 3 3 243
The odds of drawing lottery ball #15 are 1 in 50. The computation is this:
Total number of ways that ball #15 can be drawn 1
------------------------------------------------------ = -----
Total number of ways that one ball can be drawn 50
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