binomial theorem has many applications...
1........ binomial theorem is heavily used in probability theory, and a very large part of the US economy depends on probabilistic analyses.
it is most useful in our economy to find the chances of profit and loss which is a great deal with developing economy.

2.....binomial theorem and distribution is used in higher mathematics and calculation.
suppose you have given an equation with have degree 28 i.e like
2x powr28 +3x powr27..................................... +3. you can find here all 28 roots of x.In certain scientific research binomial is very helpful to solve impossible equations.if you have seen einstein equations there is a lot use of binomial theorem.thats why we have now very great theories and laws by sir albert einstein.
3.....moreover binomial theorem is used in forecast services .the future weather forcasting is impossible without binomial theorem.the disaster forecast is also depend upon binomial theorems.
4...... the selection is the most using application in our life.popularly known iit uses this theorem to give ranks to the candidates..
5......the probability will be impossible without binomial distribution.
6.... it is used in architecture in giving shape and determining the areas of infrastructure to find about the amount of material to be use in that. it help in the estimation and to find the total expenditure to build the building .so all financial sites depend indirectly on binomial theorem.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty