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Hopefully you see where this is going To find seven unique spaces for seven unique spots in which the order matters, we will have: 7 6 5 4 3 2 1 = 5,040 possible arrangements The answer to the question, therefore, is E The factorial argument we just walked through is essentially a longhand version of the formulas we are about to discuss The point of this explanation is that, even if you don t remember the specific formulas to use, you can combine the concept of the factorial with your own mathematic reasoning to work through most combination and permutation problems

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documentwrite(lastModgetMonth() + "-" + lastModgetDate() + "-" + lastModgetFullYear();

When we refer to combinations instead of permutations, we are talking about groupings in which order does not matter, eg, a red sock and a green sock instead of a red sock and then a green sock In the following formula, C stands for the total number of possible combinations, n stands for the total number of elements involved (eg, 7 socks), and k is the subset of unordered elements taken from n (eg, 3 socks out of the 7): Ck = n! k !(n k )!

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This formula may look imposing, so let s apply it to a problem: A sock drawer contains seven socks, each one a different solid color The colors of the socks are red, orange, yellow, green, blue, indigo, and violet If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks A 12 B 15 C 21 D 36 E 42 You could write out every possibility and solve this problem that way, but it is almost certainly faster to use the formula In this case, n = 7 and k = 2: Ck = n! 7! = = 7 ! = 7 6 5 4 3 2 = 7 6 = 42 = 21 k !(n k )! 2 !(7 2)! 2 !(5)! 2 5 4 3 2 2 2

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Note that it was not necessary to calculate 7! out to 5,040 By canceling out common elements in the numerator and denominator, we were able to produce an equation that was quite simple to calculate Most combination problems you see on the GMAT will work out smoothly like this; the test writers figure that if you can use this formula correctly, they don t need to test your multiplication skills

$107

11 You still need to call the function Switch to your HTML file 12 In the head section, before your existing script entry, create a <script> section using the src attribute that holds scriptjs

Just for a visual verification, let s consider how we would have worked this problem by brute force: RO RY RG RB RI RV OY OG OB OI OV YG YB YI YV GB GI GV BI BV IV

Add up the combinations: 6 + 5 + 4 + 3 + 2 + 1 = 21 Clearly, either method works for a problem of this scope One interesting thing to note with combinations is that picking 2 and leaving 5 behind is mathematically the same thing as picking 5 and leaving 2 behind The formula for the latter situation would look like:

13 Now scroll to the end of your body section As the last line of the body, create a script section calling the pageDate( ) function

n! 7! = = 7 ! = 7 6 5 4 3 2 = 7 6 = 42 = 21 k !(n k )! 5 !(7 2)! 5 !( 2)! 5 4 3 2 2 2 2

Now let s move on to a slightly more complicated situation, in which the order of the elements matters

14 Save and view the page in your browser Notice that the date is displayed in your browser Also notice that it is off by one month This is shown in the next illustration This is because programming languages start counting at 0 Thus January is month 0, while December is month 11 The simple fix is to add one 1 the month returned

When order matters, the number of permutations is almost always larger than the equivalent number of unordered combinations The formula for permutations, using the same variables of n for the total number of elements involved and k as the ordered subset of n, is as follows:

n! (n k )!

15 Switch back to your js file 16 Surround the existing lastModgetMonth( ) with a set of parentheses

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