 | Joseph Ficklin - Algebra - 1874 - 446 pages
...(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 of n things, taken n — r at... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...number of n things taken r at a time.* r-\-\ 5. The number of the combination* of n things when taken r at a time is equal to the number of combinations of the same n things when they are taken M—r at a time.\ * To ßnd tfic number of combinations thai can... | |
 | Robert Potts - 1879 - 668 pages
...number of n things taken r at a time.* r+l 5. The number of the combination» of n things when taken r at a time is equal to the number of combinations of the same n thing» when they are taketi •}i—r at a time.\ * To find the number of combinations that... | |
 | Great Britain. Education Department. Department of Science and Art - 1886 - 640 pages
...equation a? — 3* + 9 = 0. (35.) 44. Show from first principles that the number of combinations of n things r at a time is equal to the number of combinations of (n — 1) things r at a time, together with the number of combinations of ('» — 1) things (r —... | |
 | Webster Wells - Algebra - 1889 - 584 pages
...n quantities taken r at a time (Art. 450) . Hence, the number of combinations of n quantities taken r at a time is equal to the number of combinations of n quantities taken n — r at a time. • EXAMPLES. 452. 1. How many changes can be rung with ten bells,... | |
 | Webster Wells - Algebra - 1890 - 604 pages
...different things taken r at a time. Q Hence, the number of combinations of n different things takeni r at a time is equal to the number of combinations of n different things taken n — r at a time. EXAMPLES. 547. 1. How many changes can be rung with 10... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
........ 115 Number of Combinations of n things r at a time ..... 117 The number of combinations of n things r at a time is equal to the number of combinations of n things n — r at a time . . .119 Number of ways in which m + n +p + ... things can be divided into... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 552 pages
...Hence the number of ways = "Cc = Ilxl0x9x8x7 = 462. 1x2x3x4x6 395. The number of combinations of я things r at a time is equal to the number of combinations of я things n—r at a time. In making all the possible combinations of n things, to each group of r... | |
 | George Egbert Fisher - Algebra - 1899 - 506 pages
...2 x 1 " '~ \r X (nr)(nrl) --3 x2 xl In 3. We have BCL = , , — | r | n — and 0 _ = That is, the number of combinations of n dissimilar things r at...of combinations of the n things n — r at a time. Tliis relation is also evident from the definition of a combination. For, every time that r things... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 506 pages
...— » • In In and .0_r= - ' \nr\n — (n — r) \n — r\r' therefore, „C, = „Cn.rThat is, the number of combinations of n dissimilar things r at a time is erjttal to the number of combinations of the n things n — r at a time. This relation is also evident... | |
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That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time. 
