In the expansion of (x + y)^5, what is the coefficient of the term in x^3 y^2?

1. The coefficient of the term carrying y to the power r is the binomial coefficient n over r. 2. Here n = 5 and the power on y is 2, so r = 2. 3. Compute 5!/(2!(5 - 2)!) = 5!/(2! times 3!). 4. That is 120/(2 times 6) = 120/12 = 10. 5. The full row of coefficients for n = 5 is 1, 5, 10, 10, 5, 1, and the third entry matches. 6. Reading 5 instead takes the coefficient of x^4 y, which is one place too early in the row. 7. The value 20 belongs to the middle of the row for n = 6, so it comes from using the wrong power. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_