 | Mathematics - 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... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...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 of r quantities which... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...is left a corresponding group of n — r things ; that is, the number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; The proposition may also be proved as follows : \n — r \n— (n — r) \n [Art.... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1894 - 596 pages
...there is left a corresponding group of nr things; that is, the number of combinations of n things r at a time is the same as the number of combinations of и things n — r at a time ; The proposition may also be proved as follows : \n "C .—. r^-, г [Art.... | |
 | George P. Lilley - Algebra - 1894 - 522 pages
...ways can 18 be selected ? Solution. Since the number of combinations of 20 different things, taken 18 at a time, is the same as the number of combinations of 20 different things taken 20 — 18, or 2, at a time ; n = 20 and r — 2. Hence, substituting in (3),... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...is left a corresponding group of n — т things ; that is, the number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time; . nn —n/r • • ^r— ^nr This result is frequently useful iu enabling us to... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 552 pages
...is left a corresponding group of n — r things ; that is, the number of combinations of n things r at a time is the same as the number of combinations of n things « — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work.... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...discussions will now be proved. 617. THEOREM I. — -The number of combinations of n symbols taken r at a time is the same as the number of combinations of n symbols taken n — r at a time. Suppose that one has n objects in an urn; if he takes r of these from... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...discussions will now be proved. 617. THEOREM I. — The number of combination» of n symMt taken r at a time is the same as the number of combinations of » symbols taken n — r at a time. Suppose that one has и objects in an urn; if he takes r of these... | |
 | George Albert Wentworth - Algebra - 1902 - 544 pages
...from 1 up to and including 7 ; so that 343. Theorem. The number of combinations of n things taken r at a time is the same as the number of combinations of n things taken \\ — г at a time. \n [я For, C„„_r = M — г j П — (п — г) This is also evident... | |
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... number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work. 
