Binomial Coefficient
The binomial coefficient, denoted ⁿCₖ or C(n, k) or (n choose k), equals n! / (k!(n-k)!). It counts the number of ways to select k successes in n trials, regardless of order.
Real World
A talent show like The X Factor choosing 3 acts from 10 finalists can be done in C(10,3) = 120 ways — the binomial coefficient counts these arrangements without caring about order.
Exam Focus
Use your calculator's nCr function to avoid factorial arithmetic errors; confirm by checking C(n,0) = C(n,n) = 1 as a sanity check.
How well did you know this?