# Permutations Sentence Examples

- And there is no originality in it; only endless
**permutations**and combinations of doctrines already known and accepted. - Every unit of the rth species which does not vanish is the product of r different units of the first species; two such units are independent unless they are
**permutations**of the same set of primary units e i, in which case they are equal or opposite according to the usual rule employed in determinants. **Permutations**and Combinations.- In particular, the number of
**permutations**of the whole stock is n!. - Y ...a n v, the summation being for all
**permutations**of the n numbers, is called the determinant of the n 2 quantities. - Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all
**permutations**, the number of transpositions necessary determining the sign to be affixed to the member. - APn 1 2 3 ' the summation being for all
**permutations**of the indices which result in different terms. The function is written (plp2p3ï¿½4n) for brevity, and repetitions of numbers in the bracket are indicated by exponents, so that (p1p1p2) is written (p1p 2). - (v.)
**Permutations**and Combinations may be regarded as arithmetical recreations; they become important algebraically in reference to the binomial theroem (ï¿½ï¿½ 41, 44)ï¿½ (vi.) Surds and Approximate Logarithms. - From the arithmetical point of view, surds present a greater difficulty than negative quantities and fractional numbers. - The number (n P r) of
**permutations**of r individuals out of a stock of n, all being distinguishable, is n`r). - The number of distinguishable
**permutations**of the whole stock is n!= (a?b!cI (ii.) A combination is a group of individuals without regard to arrangement. - The intervention of the Curia, which hitherto had been hostile to Casimir because of his steady and patriotic resistance to papal aggression, was due to the
**permutations**of European politics. - Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials,
**permutations**, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers. **Permutations**of the n numbers I, 2, 3, ...