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10 cards from this deck
Arrangements: order matters; Selections: order doesn't matter
Combinations
Number of ways to choose rrr objects from nnn (order unimportant)
nCr=n!r!(n−r)!^nC_r = \frac{n!}{r!(n-r)!}nCr=r!(n−r)!n!
Calculate selections for each group, then multiply
2n2^n2n
Always 1
Sum of the two numbers directly above it
nCr=n−1Cr−1+n−1Cr^nC_r = ^{n-1}C_{r-1} + ^{n-1}C_rnCr=n−1Cr−1+n−1Cr for 0<r<n0 < r < n0<r<n
(nr)\binom{n}{r}(rn)
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