 | Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...Progression, and insert 4 Harmonic Means between 2 and 12. 8. Prove that 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. How many different sets at lawn-tennis might be formed out of a party... | |
 | George Albert Wentworth - Algebra - 1891 - 544 pages
...including 7 ; so that 111 12X11X10X9х8 [5[7 1X2X3X4X5 792. 382. Theorem. The number of selections of n things taken r at a time is the same as the number of selections of и things taken n — r at a time. For С [П - }П -0 •Г OTI ^п,п-Т - i - ¡... | |
 | George Albert Wentworth - 1898 - 112 pages
...r. Thus, I12 _ 12 x 11 x 10 x 9 x 8 _ [5[7 ~ 1X2X3x4X5 " 29. Theorem. The number of selections of n things taken r at a time is the same as the number of selections of n things taken n — r at a time. \n \n /~1 • I — __ I — l -r\r This is also... | |
 | George Albert Wentworth - Algebra - 1902 - 544 pages
...factors of Ц2 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... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 290 pages
...г-; -- 7 - r: — ; > (n — r) ! (n — r) ! r ! it follows that the number of combinations of n things taken r at a time is the s.ame as the number taken n — r at a time. 161. Binomial coefficients. It may be noted that the formula for „Cr is the coefficient of the (r... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...••• (r + 1) = nl nn~r = (n - r}\ ~ (n - r)!r! it follows that the number of combinations of n things taken r at a time is the same as the number taken n — r at a time. This is evident in any practical example, since the number of ways in which r things may be selected is evidently... | |
 | H.L. Rietz, A.R. Crathorne - 1919 - 476 pages
...С = n' " r Since (и- г)! (nr)!rt' it follows that the number of combinations of и things taken / at a time is the same as the number taken n — r at a time. 135. Binomial coefficients. It may be noted that the formula for „(7r is the coefficient of the (r... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1919 - 300 pages
...(n — r) !, we get _ n! Since __, (n — r) ! r ! it follows that the number of combinations of n things taken r at a time is the same as the number takeii n — r at a time. 135. Binomial coefficients. It may be noted that the formula for nCr is the... | |
 | Arthur Sullivan Gale, Charles William Watkeys - Functions - 1920 - 457 pages
...arranged, so that n(n — 1) . . . (n — r 4- 1) ~ ~~ r! Theorem 2. The number of combinations of n things taken r at a time is the same as the number of combinations of n things taken n - r at a time. Multiplying numerator and denominator of the formula... | |
 | William Le Roy Hart - Algebra - 1926 - 412 pages
...things, we leave, or set aside, (n — r) of the things. Hence, the number of combinations of n different things taken r at a time is the same as the number of combinations of n different things taken (n — r) at a time. That is, „C, = nCn_r. (6) Formula... | |
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To show that the number of combinations of n things taken i at a time is the same as the number taken n — r at a time. 
