"Arial$qu wS%$"Arial$qu wQ1 KeyContent1 Factorial number of n, n! ..."... equals n*(n-1)*(n-2)*...*3*2*18An arrangement of n things taken r at a time ...... is an injective mapping from the initial natural set n_ ((=1, ..., n)) into the set containing the n "things". ((Order does matter : (a, c, b) does not equal (b, c, a) ))RHow many arrangements of n things taken r at a time are there ? V(n,r) =? n! / (n-r)!7A combination of n things taken r at a time ...... is a strictly increasing mapping from the initial natural set n_ ((=1, ..., n)) into the ordered set containing n "things". ((Order does _not_ matter : {a, c, b} = {b, c, a} ))RHow many combinations of n things taken r at a time are there ? C(n,r) =?2n! / (r! (n-r)!) := "binomial n choose r"!A permutation of n things ...{... is a bijective mapping from the initial natural set n_ into a set containing n elements. (( P(n) = V(n,n) )):How many permutations of n things are there ? P(n) =?n!(A cyclic permutation of n things ...... is a class of bijective mappings from the initial natural set n_ to a set of n "things", as per the "cyclic equivalence" relation. ... is a class of "Bij(n_ , A) / ~"BHow many cyclic permutations of n things are there ? P(n) =?(n - 1)!IAn arrangement with repetitions of n things taken r at a time ...\... is any mapping from the initial natural set n_ into a set containing n "things".gHow many arrangements with repetitions of n elements taken r at a time, are there ? V*(n,r) =?m^nQA combination with repetitions of n things taken r at a time, C*(n,r) ...f... is an increasing mapping from the initial natural set n_ into a set containing n "things".pHow many combinations with possible repetitions of n elements taken r at a time, are there ? C*(n,r) =?binomial "n+r-1 choose r"How many permutations with repetitions of n elements taken (r of them) m1,...,mr at a time, are there ? P*(n;m1...mr) =?m! / (m1! * ... * mr!)\SETS\AUGUST.B1