<p>To what extent do counting problems show up on the SAT? </p>
<p>Gruber’s doesn’t talk about counting problems at all.</p>
<p>Sparknotes gives permutations and combinations a very thorough treatment - a little too thorough? </p>
<p>Barron’s only talks about the fundamental counting principal.</p>
<p>Rocket Review goes into some detail about counting and indistinguishable objects. </p>
<p>Princeton Review has at least one problem involving a cyclic permutation. </p>
<p>Nova’s Math Bible covers everything from counting to permutations to combinations to cyclic permutations to permutations/combinations with indistinguishable objects. Overkill? </p>
<p>The Blue Book only has questions that can be solved using the fundamental counting principal. Some of the counting problems involve indistinguishable objects. I have never seen a BB problem that involves a formula like nPr or nCr … </p>
<p>As you can see, I am very confused about counting problems. </p>
<p>To the SAT tutors out there: What exactly can I expect on test day? Just fundamental counting principal problems? </p>
<p>Or will there be permutation/combination problems on the SAT that necesitate the use of a formula - e.g. nPr or nCr?</p>
<p>You just need the basic counting principle (where you multiply the number of options for each decision you make).</p>
<p>Any SAT problem that COULD be solved by applying nPr or nCr can easily be solved by listing the possibilities in an organized way. So if you already know those combinatoric concepts, you may get a chance to use them, but you can still get a perfect score without them. </p>
<p>But the counting principle is a must.</p>
<p>Here’s one to play with: The number 8558 is an example of a positive, four-digit EVEN palindrome. (A palindrome is a number that has the same value when you reverse its digits.) How many such numbers are there?</p>
<p>By the way, IceQube: you do not sound confused at all!</p>
<p>The answer to pckeller’s problem does appear to be 40. I initially got 50, but I later realized that the last digit (and thus the first digit) cannot equal 0 (otherwise it would be a 3 digit number). </p>
<p>For the last number, there are a total of 4 possibilities. The number is even, so you can put a 0, 2, 4, 6, or 8 there. But the number is a palindrome; the last digit must match the first digit. But you can’t have 0 as the first digit. There are a total of 4 possibilities for the last number.</p>
<p>There is only 1 possibility for the first number - the first number must match the last number.</p>
<p>For the two digits in between there are 10 possibilities for one digit and only 1 possibility for the other digit, because the two digits in between must match. </p>
<p>Yes – how many positive even four digit palindromes are there? And Yes, it’s 40. Note that you can do this with the counting principle or in fact just by listing…</p>