 | Alfred Wrigley - 1845 - 222 σελίδες
...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 .... | |
 | Isaac Todhunter - 1858 - 530 σελίδες
...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 σελίδες
...numerator 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...at a time. The number of combinations of n things taken nr at a time is w(n _!)(«- 2) ...... {»-(nr) + l} \nr *~* ,(.-l)(.-«) ...... (r + l)m —... | |
 | Isaac Todhunter - 1865 - 650 σελίδες
...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 σελίδες
...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... | |
 | James Hamblin Smith - 1870 - 478 σελίδες
...n(nl) (n-r+1); .'. \r.Cr---n(nl) (n-r+1); „ _ n(nl) (n-r+I) .. .,- - • ^ 409. To shew that the number of combinations of n things taken r at a time is the same as the number taken n- r ni u time. r =n.(»-I) (nr + 1). "~ 1.2.3 r ' „ n.(nl) {n-(nr) + l} **-*- 1.2.3 (nr) _n.(nl)... | |
 | Joseph Ficklin - 1874 - 446 σελίδες
...-A |r But Pr=ra(nl)(w-2)(M-3) .... (n-r+1) (464); _я(я-1)(я-й)(п-3) ---- (nr .. Or_ r; 469. The number of combinations of n things, taken r at a time, is equal to the number of combinations of n things, taken n — r at a time. Denote the number of combinations... | |
 | James Hamblin Smith - 1879 - 144 σελίδες
...to the number or by converting it into the septenary scale. ч 10. Find the value of r for which the number of combinations of n things taken r at a time is the greatest. EXERCISE— XCIII. 1. Resolve into factors : (1) Л (2) ж'-Зж2-] 2. Solve the equations... | |
 | C R. Lupton - 1879 - 194 σελίδες
....-.P= 1.2.3. . . .p . 1 . 2 . 3 . . . . ; . 1 . 2 . 3 . . . . 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... | |
 | Webster Wells - 1879 - 468 σελίδες
...by [j^ or n (n — 1) (n — 2) (n — r+ï) \r (3) 396. The number of combinations of n quantities, taken r at a time is the same as the number of combinations of n quantities taken n — r at a time. For, it is evident that for every combination... | |
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The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time. 
