<Tr> <Th> Category </Th> </Tr> <Tr> <Td> </Td> <Td> () (\ displaystyle (\ \ choose \)) (\ \ choose \) </Td> <Td> combination; binomial coefficient n choose k combinatorics </Td> <Td> (n k) = n! / (n − k)! k! = (n − k + 1) ⋯ (n − 2) ⋅ (n − 1) ⋅ n k! (\ displaystyle (\ begin (pmatrix) n \ \ k \ end (pmatrix)) = (\ frac (n! / (n-k)!) (k!)) = (\ frac ((n - k + 1) \ cdots (n - 2) \ cdot (n - 1) \ cdot n) (k!))) means (in the case of n = positive integer) the number of combinations of k elements drawn from a set of n elements . (This may also be written as C (n, k), C (n; k), C, C, or ⟨ n k ⟩ (\ displaystyle \ left \ langle (\ begin (matrix) n \ \ k \ end (matrix)) \ right \ rangle).) </Td> <Td> (36 5) = 36! / (36 − 5)! 5! = 32 ⋅ 33 ⋅ 34 ⋅ 35 ⋅ 36 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 = 376992 (\ displaystyle (\ begin (pmatrix) 36 \ \ 5 \ end (pmatrix)) = (\ frac (36! / (36 - 5)!) (5!)) = (\ frac (32 \ cdot 33 \ cdot 34 \ cdot 35 \ cdot 36) (1 \ cdot 2 \ cdot 3 \ cdot 4 \ cdot 5)) = 376992) <P> (. 5 7) = − 5.5 ⋅ − 4.5 ⋅ − 3.5 ⋅ − 2.5 ⋅ − 1.5 ⋅ − . 5 ⋅ . 5 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 = 33 2048 (\ displaystyle (\ begin (pmatrix). 5 \ \ 7 \ end (pmatrix)) = (\ frac (- 5.5 \ cdot - 4.5 \ cdot - 3.5 \ cdot - 2.5 \ cdot - 1.5 \ cdot -. 5 \ cdot . 5) (1 \ cdot 2 \ cdot 3 \ cdot 4 \ cdot 5 \ cdot 6 \ cdot 7)) = (\ frac (33) (2048)) \, \!) </P> </Td> </Tr> <P> (. 5 7) = − 5.5 ⋅ − 4.5 ⋅ − 3.5 ⋅ − 2.5 ⋅ − 1.5 ⋅ − . 5 ⋅ . 5 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 = 33 2048 (\ displaystyle (\ begin (pmatrix). 5 \ \ 7 \ end (pmatrix)) = (\ frac (- 5.5 \ cdot - 4.5 \ cdot - 3.5 \ cdot - 2.5 \ cdot - 1.5 \ cdot -. 5 \ cdot . 5) (1 \ cdot 2 \ cdot 3 \ cdot 4 \ cdot 5 \ cdot 6 \ cdot 7)) = (\ frac (33) (2048)) \, \!) </P> <Tr> <Td> </Td> <Td> (()) (\ displaystyle \ left (\! \! (\ \ choose \) \! \! \ right)) \ left (\! \! (\ \ choose \) \! \! \ right) </Td> <Td> multiset coefficient u multichoose k combinatorics </Td> <Td> ((u k)) = (u + k − 1 k) = (u + k − 1)! / (u − 1)! k! (\ displaystyle \ left (\! \! (u \ choose k) \! \! \ right) = (u + k - 1 \ choose k) = (\ frac ((u + k - 1)! / (u-1)!) (k!))) <P> (when u is positive integer) means reverse or rising binomial coefficient . </P> </Td> <Td> ((− 5.5 7)) = − 5.5 ⋅ − 4.5 ⋅ − 3.5 ⋅ − 2.5 ⋅ − 1.5 ⋅ − . 5 ⋅ . 5 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 = (. 5 7) = 33 2048 (\ displaystyle \ left (\! \! (- 5.5 \ choose 7) \! \! \ right) = (\ frac (- 5.5 \ cdot - 4.5 \ cdot - 3.5 \ cdot - 2.5 \ cdot - 1.5 \ cdot -. 5 \ cdot . 5) (1 \ cdot 2 \ cdot 3 \ cdot 4 \ cdot 5 \ cdot 6 \ cdot 7)) = (. 5 \ choose 7) = (\ frac (33) (2048)) \, \!) </Td> </Tr>

What means the same as a/b