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10 cards from this deck
An unordered selection of items where order doesn't matter.
An ordered arrangement of items where sequence matters.
nCr=n!r!(n−r)!nCr = \frac{n!}{r!(n-r)!}nCr=r!(n−r)!n!.
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.
(nr)+(nr−1)=(n+1r)\binom{n}{r} + \binom{n}{r-1} = \binom{n+1}{r}(rn)+(r−1n)=(rn+1).
Order does not affect the count of unique selections.
Used to calculate outcomes without regard to order.
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