Final answer:
The coefficients of the terms of (a + b)^n can be found using combinations, Pascal's Triangle, and the Binomial Theorem. These methods relate to computing binomial coefficients, which are crucial in the expansion of a binomial expression and probability theory.
Step-by-step explanation:
The coefficients of the terms of (a + b)^n can be found by using Pascal's Triangle, Combinations (also known as binomial coefficients), and by applying the Binomial Theorem. The Binomial Theorem states that (a + b)^n can be expanded as a series of terms in the form of a^n, n*a^(n-1)*b, to terms involving b^n, where each term's coefficient is determined by the binomial coefficients. These coefficients are exactly the numbers found in Pascal's Triangle or can be calculated using combinations as n choose k (written as C(n, k) or nCk), which gives the number of ways to select k items from n options without regard to order.Moreover, the series expansion provided by the Binomial Theorem holds not only for algebraic expressions, but also gives a very accurate approximation for functions where terms can be small, such as those involving low velocities. In probability theory, the concept of combinations and the binomial distribution come into play when dealing with independent trials and the calculation of the probability distribution's mean and standard deviation.