<p>Well, difficult to me, although I believe it's a fairly simple combinatorics problems solved using the binomial distribution theorem...</p>
<p>A professor gives his class a list of 20 study questions, from which he will select 8 to be answered on the final exam. If a given student knows how to answer 14 of the questions, what is the probability that the student will be able to answer all 8 questions?</p>
<p>Any help is appreciated.</p>
<p>Thanks,</p>
<ul>
<li>John</li>
</ul>
<p>Think of the 14 questions the student knows as 'red', the remaining (20-14) as 'green'. The problem then is equivalent to 'What is the probability of picking 8 consecutive red questions from the pool of 20?'</p>
<p>Answer: (14/20)(13/19)(12/18) ..... (7/13) = 0.0238</p>
<p>How many ways are there to choose 8 questions from the 20
Simply put :20 C 8</p>
<p>How many was are there to choose 8 questions when you know 14</p>
<p>Likewise : 14 C 8</p>
<p>So probability would just be 20C8 / 14C8= (665280/27907200)=0.0238</p>
<p>Permutations..ding! ding!</p>
<p>Any TI calculator can do that in 2 seconds.</p>
<p>use binomial theorem whenever there's 4 #'s</p>
<p>20c8/14c8 (10char)</p>
<p>actually, it's 14c8/20c8. you two both mixed up the numerator/denominator... :(</p>