Question 1091827
Please help...
Find the coefficient of the given term in the binomial expansion
x^11y^3 term, (x+y)^14
Thank you. 
<pre>First of all, it’ll have to be determined what TERM number produces {{{x^11}}}.

Since the exponent on the binomial is 14, it follows that there will be 15 (FIFTEEN) terms, and the term number containing {{{x^11}}} will be the 15th – 11th term, or the 4th term.

To find a specific term in a BINOMIAL EXPANSION, we use the following formula: 
{{{(a + b)^n = ""[n]C[r - 1](a)^(n-(r-1))(b)^(r-1)}}}, where r = term number 
{{{(x + y)^14 = ""[14]C[4 - 1](x)^(14 - (4 - 1))y^(4 - 1)}}}

As seen above, the 4th term of the sequence will have the following coefficient on x: {{{"" [14]C[4 - 1]}}}. This results in: {{{highlight_green(matrix(1,3, "" [14]C[3], "=", highlight(364)))}}}  
You could also check PASCAL’S triangle and look for the coefficient for the 4th term of a BINOMIAL EXPANSION with a binomial that’s being raised to the 14th power. 
This is 364.