<p>I will be taking the Math II test in October 2012 and I have been getting consistent scores on practice tests. However, I continue to have trouble with probability and combanitorics i.e. coin flips, creating groups of people, etc. Can anyone point me to a good site or resource that explains these topics well? I own the Barron's book and the explanations of these topics are pretty bad. In most cases they just tell me to write out all of the possibilities for coin flip problems which is too time consuming.</p>
<p>Please provide me with a good explanation / example so I can start getting these questions right.</p>
<p>Here are some of the questions I have trouble with:</p>
<p>A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear?</p>
<p>A committee of 5 people is to be selected from 6 men and 9 women. If the selection is made randomly, what is the probability that the committee consists of 3 men and 2 women?</p>
<p>1) The number of ways 2 heads can appear is obviously three (exactly one toss of three has to be a tails). The total number of possibilities would be 8, but since 3 tails is ruled it it is 7. So the probability is 3/7.</p>
<p>2) The number of ways of choosing 3 men is 6!/(3!3!)=20. The number of ways of choosing 2 women is 9!/(7!2!)=36 giving 720 total favorable outcomes. Divide by the 15!/(5!10!) ways of choosing people to get your probability.</p>