Combinations (HSC SSCE Mathematics Extension 1): Flashcards

An unordered selection of items where order doesn't matter.

An ordered arrangement of items where sequence matters.

$nCr = \frac{n!}{r!(n-r)!}$.

The product of all positive integers up to n.

5C3 = \frac{5!}{3!(5-3)!} = 10.

Selecting committee members from a group.

To visualize relationships of binomial coefficients.

$\binom{n}{r} + \binom{n}{r-1} = \binom{n+1}{r}$.

Order does not affect the count of unique selections.

Used to calculate outcomes without regard to order.