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<p>[QUOTE=&quot;-jeffB, post: 2642721, member: 27832&quot;]Not me, at least not today. Combinatorics was fun, but that was a few decades ago.</p><p><br /></p><p>I got a radar note a few years ago when I sold some silver at a coin show. I posted it here, and someone observed that it was also a trinary. I pointed out that that&#039;s not a big deal -- for a radar (or a repeater), you only get to randomly choose the first four digits, and those determine the second four. I guessed at the time that something like one in seven radar notes would be trinary, but I think that&#039;s low -- when you pick the first three digits, there&#039;s a significant chance two of them are repeats, and even if they aren&#039;t, you&#039;ve got a three-in-ten chance of duplicating one in the fourth digit.</p><p><br /></p><p>Actually, this should be pretty simple. How many ways can you get four different digits? 10 (first can be 0-10) times 9 (9 left to choose from) times 8 times 7 = <b>5040</b>, or just over half the 10,000 possible combinations. <b>Most</b> of the remainder will be &quot;trinaries&quot; (three different digits), minus the number of binaries and solids.</p><p><br /></p><p>How many solids are there? 10. 00000000 through 99999999.</p><p><br /></p><p>How many binaries? That&#039;s trickier, and my trickery carries some 30 years of rust. But thinking sideways, there are 16 four-digit &quot;true&quot; binary numbers, and a binary SN just has to have two different digits, so there are 10 possibilities for the first digit and 9 for the second. So I&#039;m guessing the number of binary radars is 10 x 9 x 16, or 1440.</p><p><br /></p><p>So, 10000 - 5040 = 4960, minus 1440 = 3520, minus 10 = 3510 -- in other words, just over one in three radars (or repeaters, same reasoning) should be trinary. About 3 in 20 radars or repeaters should be binary. No radars or repeaters will be solids, because they&#039;d be marketed as solids, not radars or repeaters!</p><p><br /></p><p>Oh, and 1 out of 16 binaries should be a radar, and 1 out of 16 of them should be a repeater. I think.</p><p><br /></p><p>Aw, man -- just when I thought I was out, you pull me back in! <img src="styles/default/xenforo/clear.png" class="mceSmilieSprite mceSmilie1" alt=":)" unselectable="on" unselectable="on" />[/QUOTE]</p><p><br /></p>

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