combinations.rkt

#lang racket/base

(define-syntax-rule (assert expr)
  (unless expr
    (raise-user-error "Assertion failed: " (quote expr))))

(define (factorial n)
  (if (zero? n)
      1
      (* n (factorial (sub1 n)))))

(define (permutations n k)
  (if (< n k)
      0
      (/ (factorial n) (factorial (- n k)))))

(define (combinations n k)
  (/ (permutations n k)
     (factorial k)))

(assert (= (combinations 7 3) 35))