- Unlike permutations, where order makes a difference, combinations of
objects occur when the order makes no difference.
- for example, in problem 2, we are told. A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a selection?"
- In this case, we don't care what order we select the books, just that we get all that we ordered.
- Notation: r choices selected from n items without regard to order is
written nCr
- nCr = n!/(n-r)!r!
- So for the above problem
n = 40
r = 8
40! 40×39×38×37×36×35×34×33×32!
40C8 = ------- = ---------------------------
(40-8)!×8! 8!× 32!
40×39×38×37×36×35×34×33
= ------------------------
8×5× 4× 2×3×6 ×7
= 39×19×37×5×17×33 = 76,904,685
- Example number 28, page 578
n = 11
r = 4
11C4 = 11!/(11-4)!4!
= 11×10×9×8/4×3×2×1
= 11×10×3
= 330
- Example, number 38 page 578
Find the number of 2 professor committees
5C2 = 10
Find the number of 10 students committees
15C10 = 3003
By the FCP then, there are 10x3003 or 30,030 different committees.