<p>What is the thirteenth term of the expansion of (x + y)17?</p>
<p>There are 18 terms in this expansion. Because of the third property, y is raised to the 13 1 = 12th power. The fourth property tells us that x is raised to the 17 12 = 5th power (since the sum of the exponents must be 17). The coefficient of this term is:</p>
<p>17C5 = 6188</p>
<p>which is also equal to</p>
<p>17C12 = 6188</p>
<p>So the thirteenth term is 6188x5y12.</p>
<p>*</p>
<p>I don't understand how did they determine that y is raised to the 12th power and x to the 5th. Why can't it be 11th and 6th as long as the sum is 17?</p>