Evaluate the binomial coefficient 9 over 7.

1. Apply the formula with n = 9 and r = 7, giving 9!/(7!(9 - 7)!) = 9!/(7! times 2!). 2. Write 9! as 9 times 8 times 7! so the 7! cancels. 3. That leaves (9 times 8)/2! = 72/2. 4. So the coefficient is 36. 5. The same answer comes from 9 over 2, because the two factorials in the denominator simply swap places. 6. Stopping at 9 times 8 gives 72, which forgets to divide by 2!. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.6 Binomial Theorem_