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" Therefore the number of permutations of n things taken r at a time is n(n -l)1n — 2)-.(n — r + 1). "
Elements of Algebra - Page 321
by Henry Sinclair Hall - 1918
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...things taken 5 at a time is to the number where 3 are taken at a time as 1 8 is to 5 ; find и. 759. The number of permutations of n things taken r at a time is equal to 10 times the number taken (1 — 1) at a time: and the number of combinations of n things...
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Algebra

Isaac Todhunter - Algebra - 1858 - 528 pages
...a time. The number of combinations of n things taken r at a time is n(nl)(n-2) (nr + l) " ~E ' For the number of permutations of n things taken r at a time is n(n — 1) (n — 2) (и — r + 1) by Art. 490; and each combination produces |_r permutations, by Art....
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Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1866 - 614 pages
...a time. The number of combinations of n things taken r at a time is n(nl)(n-2) (n-r+ 1) ~Tr " ' For the number of permutations of n things taken r at a time is n(n— l)(n — 2) (n — r+l), by Art. 490; and each combination produces \r_ permutations, by Art. 493;...
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Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1870 - 626 pages
...a time. The number of combinations of n things taken r at a time is n(nl)(n-2) (re-r + 1) lr " For the number of permutations of n things taken r at a time is n(n—l)(n-2) (n— r+1), by Art. 490; and each combination produces \r permutations, by Art. 493 ;...
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Elementary Algebra

James Hamblin Smith - Algebra - 1870 - 452 pages
...additional factor the number of factors is equal to the number of things taken at a time, it follows that the number of permutations of n things taken r at a time is the product of the factors w.(nl)(n— 2) (n—r+}~). ANSWERS. I. (Page 10.) 2. a+3b + 2c. 3. 4. 8«...
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Algebra

Isaac Todhunter - 1870 - 818 pages
...The number of combinations of n things taken r at a time is n(nl}(n-2) (n-r+l) ._ ^ - -....._. For the number of permutations of n things taken r at a time is n(n—l)(n—2) (n—r+l), by Art. 490; and each combination produces \r permutations, by Art. 493...
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Algebra for Beginners: With Numerous Examples

Isaac Todhunter - Algebra - 1872 - 350 pages
...though different permutations, form the same combination, so also do ae and ca, and be and cb. 417. The number of permutations of n things taken r at a time is n(n- l)(n- 2) (n- r + 1). Let there be n letters а, b, с, d, ; we shall first find the number of permutations...
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Algebra for Beginners: With Numerous Examples

Isaac Todhunter - Algebra - 1876 - 350 pages
...of combinations ofn. thingt taken r . n(nl)fn-2)...(nr + l) at a lime is -* ' A — - -. TA ~ 17 For the number of permutations of n things taken r at a time is n (n — l)(n— 2)...(n-r+l)by Art. 417; and each combination produces r permutations by Art. 420;...
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Algebra

C R. Lupton - 1879 - 194 pages
...r &c. n or P= [p [£ [r_ SiO. 186. The number of Combinations of n things taken r at a time is For the number of permutations of n things taken r at a time is and each combination produces V permutations ; hence if Or denote the number of combinations of n things,...
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A Synopsis of Elementary Results in Pure and Applied ..., Volume 1, Part 1

George Shoobridge Carr - Mathematics - 1880
...permutations of n + 1 things ; therefore, &c. See also (233) for the mode of proof by Induction. 95 The number of permutations of n things taken r at a time is denoted by P (n, r). P (n, r) = n(nl)(n-2) ... (n—r+ï) = пм. By (94) ; for (те— г) things...
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