https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_1_2007-2008_Problems/Problem_1&feed=atom&action=history Mock AIME 1 2007-2008 Problems/Problem 1 - Revision history 2022-10-03T11:13:09Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_1_2007-2008_Problems/Problem_1&diff=24469&oldid=prev Azjps: sol 2008-04-02T21:16:36Z <p>sol</p> <p><b>New page</b></p><div>== Problem ==<br /> What is the coefficient of &lt;math&gt;x^3y^{13}&lt;/math&gt; in &lt;math&gt;\left(\frac 12x + y\right)^{17}&lt;/math&gt;?<br /> <br /> == Solution == <br /> In a [[binomial expansion]], the sum of the degrees of the power of each of the two terms must sum to the power being raised to, here &lt;math&gt;17&lt;/math&gt;. However, &lt;math&gt;3 + 13 = 16&lt;/math&gt;, contradiction; so there does not exist such a term, and the answer is &lt;math&gt;\boxed{000}&lt;/math&gt;.<br /> <br /> == See also ==<br /> {{Mock AIME box|year=2007-2008|n=1|before=First question|num-a=2|source=196980}}<br /> <br /> [[Category:Intermediate Algebra Problems]]</div> Azjps