The coefficient of $$x^{7}$$ in the expansion of $$(1 - x^{2} + x^{3})(1 + x)^{10}$$ is:

We need to find the coefficient of $$x^7$$ in the expansion $$(1-x^{2}+x^{3})(1 + x)^{10}$$ 

Now, $$(1 + x)^{10}$$ will have all the powers of x from 0 to 10. Multiplying these powers by 1, $$x^2$$ and $$x^3$$ will yield different results but we are interested in finding only the coefficient of $$x^7$$. When we multiply $$x^7$$ of $$(1 + x)^{10}$$ by 1, $$x^5$$ of $$(1 + x)^{10}$$ by $$x^2$$ and  $$x^4$$ of $$(1 + x)^{10}$$ by $$x^3$$ we will get $$x^7$$. coefficient of $$x^7$$ in $$(1 + x)^{10}$$ is $$10C_7$$ = 120, coefficient of $$x^5$$ in $$(1 + x)^{10}$$ is $$10C_5$$ = 252, coefficient of $$x^4$$ in $$(1 + x)^{10}$$ is $$10C_4$$ = 210 adding 120 and 210 and subtracting(since $$x^2$$ has a negative sign) 252 we get coefficient of $$x^7$$ as 78

Therefore our answer is option 'B'