Can't figure out this problem! Help! (Math IIC, SAT II)

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1

<p>This is the only problem I can't figure out in the Math IIC practice test from "Real SAT Subject Tests" by CollegeBoard.</p>

<p>The problem reads:</p>

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<p>In how many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people?</p>

<p>a) 120 .......... b) 210 .... c) 240......... d) 5,040....... e) 14,400</p>

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<p>The answer is A. I just don't understand why!</p>

<p>Can someone help me?</p>

<p>Thanks!</p>

<p>~zarin</p>

2

<p>This is direct combinatorics problem. The general formula to select r items from n items is n!/r!(n-r)! In this problem, when you put seven in one group the other gets three! The answer is 10!/(7!<em>3!) = 8</em>9<em>10/3</em>2*1 = 120.</p>

3

<p>Oh, right.. Yeah.. Now I remember that equation--learned it in AP Stats, but for the life of me couldn't remember it!</p>

<p>Thanks so much!</p>

4

<p>Also, TI-83s have a choose function under Math/PRB/nCr. You'd type in 10 nCr 7. :D</p>