FREE UPCAT REVIEW MATERIAL -- Permutation, Combinations and Probabilities

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This is one of my favorite topics to teach because the mathematical concepts are so easy to understand you can almost hold them with your hands.

It looks daunting on paper but we explain it a very tangible way during our UPCAT reviews. But, don't let your math melodrama start, if it becomes too difficult or scary, read UPCAT Review -- Dealing with Math

Example:

In how many ways can the first, second and third prize winners be chosen from 5 contestants in an essay writing contest? 

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Explanation: 

How many options do you have in picking the 1st prize winner out of five? You may choose writer A, B, C, D or E so 5.

How many options do you have in picking the 2nd prize winner out of five? Note that in a contest, each participant only has one entry so the 1st prize winner CANNOT be the 2nd prize winner at the same time. So you have 4 options for the 2nd prize winner.

How many options do you have in picking the third prize winner out of five? As the 1st and 2nd prize winners cannot be the 3rd prize winner, you have 3 options for the 3rd prize winner.

According to the fundamental counting principle, you just multiple the number of options per pick and you have the total number of ways. 
Number of ways = (# of options for pick 1) x (# of options for pick 2) x (# of options for pick 3) and so on...
=5x4x3
=60 

Try the pre-test then read the chapter and finally, do the post-test and see how well you improve. In our UPCAT review, it is not a problem getting zero in the pre-test but it is a problem if you still get less than half after 4 hours of teaching. 

I will post the answers to the pre-test and post-test after you guys leave comments. Leave your questions in the comments, too! If I receive no comments, the answers will not be revealed. If there are typos, please let me know. The attachment is a draft.

The full review material is downloadable here (and yes, feel free to pass around FB or via email, just don't alter the contents please):

UPCAT Review Math 6of16.pdf

For more reviewers, visit MORE FREE UPCAT REVIEWERS . For more study tips on Statistics and Probabilities, go MORE STATISTICS AND PROBABILITIES EXAMPLES.