Question 986242
What is the coefficient of {{{x^3y^4}}} in the binomial expansion of {{{(x+y)^7}}}?

Thank you kindly.
<pre>For this problem, the formula to determine a specific term in a Bernoulli/Binomial expansion should be used. It states:
{{{(a + b)^n =" "[n]C[r - 1](a)^(n-(r-1))(b)^(r-1)}}}, where r = term number 

We have: {{{(x + y)^7}}}, which becomes: {{{(x + y)^7 =" "[7]C[r - 1](x)^(7-(r-1))(y)^(r-1)}}}
The expression: {{{x^3y^4}}}, without its coefficient, occurs at the term where {{{x^3y^4 = (x)^(7 - (r - 1))y^(r - 1)}}}
Thus, 3 = 7 - (r - 1)
3 = 7 - r + 1
3 = 8 - r
3 - 8 = - r 
- 5 = - r
r, or term number where {{{x^3}}} occurs = {{{(- 5)/(- 1)}}}, or 5 

Confirming this, and as seen above, {{{y^4}}} occurs at {{{y^(r - 1)}}}, and so:
4 = r - 1
4 + 1 = r
r, or term number where {{{y^4}}} occurs = 5 

This means that the expression: {{{x^3y^4}}} without its coefficient occurs at the 5th term

We now have: {{{" "[7]C[r - 1](x)^(7-(r-1))(y)^(r-1)}}}, with r or term number being 5
This becomes: {{{" "[7]C[5-1](x)^(7-(5-1))(y)^(5-1)}}} 
{{{" "[7]C[4](x)^(7-4)(y)^(5-1)}}} 
{{{35x^3y^4}}}

As seen the coefficient of {{{x^3y^4}}} in the expansion of: {{{(x + y)^7}}} is: {{{highlight_green(35)}}}