<p>In a date auction game 8 of the participants are to be auctioned. There are 4 boys and 4 girls. The turn out is 30 participants 16 of whom are boys leaving the rest (14) of them as girls. What is the number of ways each auctioned person can be paired with the opposite sex?</p>
<p>I'm totally stumped. someone please help....</p>
<p>Thanks in advance.....</p>
<p>Okay, first of all, this must be from a practice book, not the real thing -- the question is phrased terribly. Are you pairing people in the audience with other people in the audience, or people on the show with people in the audience, or just people in the show with other contestants? </p>
<p>Anyway, I imagine that you are pairing people in the show with people in the audience. In that case, follow this method:</p>
<ol>
<li>Draw two sets of two blanks. These represent the two "seats" in the pair.
___ * ____</li>
<li>The first set of blanks represents seat one, a guy, and seat two, a girl from the audience. The second set represents seat one, a girl, and seat two, a guy from the audience.</li>
<li>You now have:
4<em>16
and
4</em>14</li>
<li>There are (4<em>16) ways to pair a boy with a girl audience member, and (4</em>14) ways to pair a girl with a boy audience member. Add those two numbers together and you get your answer.</li>
</ol>
<p>That's just my best guess!!!</p>
<p>Here is another hard problem:</p>
<p>To control the quality of their product, the bright light company inspects three light bulbs out of each batch of ten bulbs manufactured. If a defective bulb is found, the batch is discarded. suppose that a batch contains two defective bulbs. what is the prpbability that the batch will be discarded?</p>
<p>I'm not sure, but I think this is the light bulb one:</p>
<p>2/10 + 2/9 +2/8=
1/5 + 2/9 +1/4= 0.6722222</p>
<p>The probability that all three selected light bulbs are not defective is
(8/10)x(7/9)x(6/8) = .46666
The probability that at least one of three selected light bulbs is defective is
1 - .4666 = .53333</p>
<p>I think the person above has the correct way of doing it or atleast one correct way of doing it.</p>
<p>Nope, I think that gcf101 is correct.</p>
<p>That's what vasudevank meant.</p>
<p>For the first question, it's the number of ways to match up the four boys with their fourteen possible dates (14<em>13</em>12<em>11) times the number of ways to match up the four girls with their sixteen possible dates (16</em>15<em>14</em>13). It comes to about a hundred million.</p>
<p>First one:</p>
<p>(16<em>15</em>14<em>13) * (14</em>13<em>12</em>11)</p>
<p>Second one:</p>
<p>1 - (8/10 * 7/10 * 6/10)</p>
<p>Alternatively, the direct method for the second one:</p>
<p>2/10 + 8/10 * ( 2/9 + 7/9 * (2/8) ) )</p>