 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...same m the two ca things are taken - — 155. The formula for the number of combinations of n 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... | |
 | George William Jones - Algebra - 1892 - 300 pages
...line be cut at four points, how many segments are formed ? at six points ? at n points ? 5. Show that the formula for the number of combinations of n things taken r at a time, may be written n\/r\(n - r)\ Hence prove that crn = cn_rn. 6. Find the number of combinations of 10 things... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1894 - 596 pages
...result being the 1 J same in tho two cases. 155. The formula for the number of combinations of n things r at a time may be found without assuming the formula for the number of permutations. Let *Cr denote the number of combinations of n things taken r at a time; and let the n things be denoted... | |
 | Faculty of Actuaries in Scotland - Insurance - 1907 - 488 pages
...Ioga6 log(/ = l If Ioga6=logi,c and logac=logcfZ, prove that (loga'/)3 = ( 19. Find the expression for the number of combinations of n things taken r at a time, without assuming that for the number of permutations. 20. How many different arrangements of... | |
 | Harold Ordway Rugg - Education - 1917 - 442 pages
...seeing now in what way he can check his experience against regularity of mathematical order. The above formula for the number of combinations of n things taken r at a time now enables us to foretell, in the case of a given number, n, of independent events working under... | |
 | Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...which contains neither x nor y. yx / 213. The Binomial Series. The binomial theorem and the symbols nCr for the number of combinations of n things taken r at a time, have no meaning except when n and r are positive integers. On the other hand we know that such... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne, J. Charles Rietz - Business - 1921 - 304 pages
...at a time are, abc, abd, acd, bed. 89. Number of combinations of things all different. Let nCr stand for the number of combinations of n things taken r at a time. The formula for nCr is found by finding the relation of nCr to nPr. Take any one combination... | |
 | Frank Loxley Griffin - Calculus - 1922 - 548 pages
...height, x in. ? [Show that your result is the arithmetical average.] § 344. Summary of Chapter XIV. The formula for the number of combinations of n things taken r at a time is derived from the formula for the number of arrangements. Besides its more important uses, it... | |
 | Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1925 - 398 pages
...permutations and combination.) 111. What is the distinction between a permutation and a combination? Deduce the formula for the number of combinations of n things taken r at a time. 112. Show that (2 + i)2 = —. when i =V1. 1 — i 113. How many terms are there in the development... | |
 | Frank Moore Colby, Talcott Williams - Education - 1922 - 922 pages
...example, the permutations of the letters а, Ъ, с taken 2 at a time are ab, ba, ac, ca, be, cb. The number of combinations of n things taken r at a time may be indicated by the symlxil C". The number of permutations of n things taken r at a time may be indicated... | |
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The general formula for the number of combinations of n things taken r at a time is C(и,r) = n\ r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time. 
