What are the uses of binomial theorem?
The binomial theorem is used to expand polynomials. So, if you’re ever working with polynomials in any area of science, the binomial theorem will make things much easier for you. More interestingly, understanding the binomial theorem is essential to understanding basic probability and combinatorics, two fields with very important real world applications. For example, if I flip a coin 5 times, the number of ways of getting 3 heads is the coefficient of x^3 in the expansion of: (1+x)^5=(1+x)(1+x)(1+x)(1+x)(1+x) This happens to be so because of the way algebra is done; just imagine that 1’s represent tails and x’s represent heads. Each time you flip you choose a 1 or an x. The coefficient of x^3 is known as Binomial(5,3) More advanced cases of what I just demonstrated lead to generating functions, which are an extremely powerful technique for solving probability questions. For example, the probability of rolling a die 5 times and having the resulting rolls add up to 15 is the coefficient
