 This is the same as the number of permutations of n things taken r at a time, and hence r!C(»,r) = P(«,r) '-- It is interesting to know that the number of combinations of n things taken r at a time is the same as the number of combinations of n things...  Elementary Functions and Applications - Page 368de Arthur Sullivan Gale, Charles William Watkeys - 1920 - 436 pagesAffichage du livre entier - À propos de ce livre
 | 1836 - 530 pages
...we reject m — n of the things, it follows that the number of combinations of от things taken n at a time is the same as the number of combinations of the same things taken m — n at a time. To find the latter of these numbers, we must observe that... | |
 | Great Britain. Committee on Education - 1853 - 1218 pages
...3- + &c. to n terms. U. Find the number of combinations of n things taken r together, and show that is the same as the number of combinations of n things taken n — r together. 3. Prove the binominal theorem in the case in which m is a positive integer, and expand (... | |
 | James Wood - 1841 - 492 pages
...gives the greatest No. of com~ binations. 288. The number of combinations of n things taken r together is the same as the number of combinations of n things taken n — r together. The number of combinations taken nr together is n (n- 1) (и-2) ... \n - (nr) + i} i Г~2... | |
 | Alfred Wrigley - 1845 - 222 pages
...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 taken r at a time is to the number taken (r— 1) at a time as 5 is to 3 ; required the values of n and r. 760. Itpvpj .... | |
 | Joseph Ray - 1852 - 408 pages
...three together, U 5*4*3=1Q. 1X2X3 AKT. :JO1>. The number of combinations of n things taken r together, is the same as the number of combinations of n things taken n — r together. The truth of this proposition is evident from the following consideration : if out of n things... | |
 | Isaac Todhunter - 1858 - 530 pages
...third term — \ — ¡5—^ ; and L • ¿ generally the coefficient of the (r + l)th term, being the number of combinations of n things taken r at a time is, by Art. 494, , n (n - 1) (n - 2) ...... (n-r+l) , ,,- i - ,i equal to — ' - -ii - , - - - - ; by... | |
 | Isaac Todhunter - 1860 - 620 pages
...and denominator of this exl» pression by I n — r it becomes . — : - . 1 * L - rn — r 495. The number of combinations of n things taken r at a time is the same as the number of them taken n — r at a time. The number of combinations of n things taken nr at a time is w(n _!)(«-... | |
 | Isaac Todhunter - 1865 - 650 pages
...theorem here that is of any importance is that •which we should now express thus : if n be prime the number of combinations of n things taken r at a time is divisible by n. (4) A passage in which Leibnitz names his predecessors may be quoted. After saying... | |
 | Isaac Todhunter - 1865 - 656 pages
...theorem here that is of any importance is that which we should now express thus : if n be prime the number of combinations of n things taken r at a time is divisible by n. (4) A passage in which Leibnitz names his predecessors may be quoted. After saying... | |
 | Isaac Todhunter - 1866 - 580 pages
...multiply both numerator and denominator of this expression by ! n — r it becomes - — *= . 495. The number of combinations of n things taken r at a time is the same as the number of them taken n — r at a time. The number of combinations of n things taken n — r at a, time is n(nl)(n-2)... | |
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