| Isaac Todhunter - Algebra - 1858 - 528 pages
...what. value of r the number of the combinations of n things taken r ai a time is greatest. Let (n)r denote the number of combinations of n things taken r at a time, (я)г_, the. number of combinations of n things taken r - 1 at a time, , . . . n-r+l . . then,... | |
| John Thompson Platts, Alfred Wrigley - Mathematics - 1861 - 482 pages
...(a) Remove the given patrol from the 36, then о ;, 35.34.33.3», 5 6o. 1.2.3.4 J •' 20. If <7m(r) denote the number of combinations of ?n things taken r at a time, Then the total number 0,n = OQ + СЙ + <7|?> + . . . + GST " + OST 1.2 I. 2.3 Similarly, Cn = 2" - i. Hence... | |
| Mathematics - 1865 - 132 pages
...the number of triangular pyramids with their bases in the planes. Solution by the PBOPOSEB. Let nCf denote the number of combinations of n things taken...then in the plane (A) the number of triangles will be m-pC3 + Pm-PC*+ (mP)pC2 = MSimilarly the number in the plane (B) will be M_3C3+ ?B_8C2+ (»-2)4C2 =... | |
| Isaac Todhunter - Probabilities - 1865 - 656 pages
...number of cases ; the corresponding number in Laplace's problem is {$ (n, r}}*, where by <f> (n, r) we denote the number of combinations of n things taken r at a time. In De Moivre's problem (n — I)1 is the whole number of cases that would exist if one face of... | |
| Isaac Todhunter - Algebra - 1866 - 614 pages
...produce ~ permutations (Art. 498), and Li thus the whole number of permutations may be found. Let (n)r denote the number of combinations of n things taken r at a time. Suppose n letters a, b, c, d, ...... ; among the combinations of these r at a time, the number... | |
| Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...things r at a time may be found without assuming the formula for the numbeB of permutations. Let "Cr denote the number of combinations of n things taken r at a time; and let the n things be denoted by the letters ^ 4 4 d, Take away a ; then with the remaining... | |
| W. J. C. Miller, D. Biddle - Mathematics - 1901 - 128 pages
...their bases in the planes. Solution by the PBOPOSEB. Let ЯCР denote the number of combinations of » things taken r at a time ; then in the plane (A) the number of triangles will be Similarly the number in the plane (B) will be »_SC3+ 2»_äC2+ (nj)jCs = N. For the combination of... | |
| Joseph William Mellor - Chemistry, Physical and theoretical - 1902 - 620 pages
...cd. But when each set consists of r things, each set can be arranged in r \ different ways. Let nC, denote the number of combinations of n things taken r at a time. We observe that the nCr combinations will produce ,,Cr xr ! permutations. This is the same thing... | |
| Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 292 pages
...combinations of а Ь с taken two at a time are ab, ас, be. 160. Combinations of things all different. Let nCr denote the number of combinations of n things taken r at a time. Then a formula can be derived for nCr by establishing the relation between nCr and nPr. Take one combination... | |
| Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 296 pages
...of а 6 с taken two at a time are ab, ас, be. 160. Combinations of things all different. Let n(7, denote the number of combinations of n things taken r at a time. Then a formula can be derived for nCr by establishing the relation between nCr and nPr. Take one combination... | |
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