 | Isaac Todhunter - Algebra - 1858 - 530 pages
...time. Thus the whole number of permutations when the letters are taken r at a time will be nr. 501. By the following method the formula for the number...assuming the formula for the number of permutations. Let (ii)r denote the number of combinations of n things taken r at a time. Suppose n letters a, b, c, d,... | |
 | Isaac Todhunter - 1860 - 620 pages
...time. Thus the whole number of permutations when the letters are taken r at a time will be n*. 501. By the following method the formula for the number...(n)r denote the number of combinations of n things takea r at a time. Suppose n letters a, b, c, d, ...... ; among the combinations of those r at a time,... | |
 | Braithwaite Arnett - 1874 - 130 pages
...harmonic mean (1— a;2)*, find the geometric mean ; determine also A and B. 10. Assuming the general formula for the number of combinations of (n) things taken (r) at a time show that the formula will give the same number whether T = 4 or r = (n — 4), verify this when... | |
 | Thomas Kimber - 1874 - 352 pages
...first, and also to nine-tenths of the sum of the second and third. Find the three numbers. 7. Prove the formula for the number of combinations of n things taken r and r together. In how many ways can I select two white balls and three red out of an urn containing... | |
 | Sir George Greenhill - Mathematics - 1876 - 318 pages
...2. Of these six sets of roots three only are distinct, and the roots Va* are a, a, a 6. Investigate the formula for the number of combinations of n things taken r at a time, without assuming the formula for permutations. A selection of c things is to be made, part from... | |
 | Thomas W. Piper - 1879 - 298 pages
...2x1=2. 2d. Three „ [3 = 3x2x1 = 6. 3d. Four „ |jt_=4x 3x2x1 = 24. 4th. » „ [n. 2. THE NÜXBER OF COMBINATIONS OF N THINGS TAKEN R AT A TIME may be found as in the following example : — Ex. 1. How many different combinations may be made of the first ten... | |
 | Thomas Kimber - 1880 - 176 pages
...first, and also to nine-tenths of the sum of the second and third. Find the three numbers. 7. Prove the formula for the number of combinations of n things taken r and r together. In how many ways can I select two white balls and three red out of an urn containing... | |
 | 1883 - 248 pages
...=0, or p = — j Also P + 1 = 2 p = 2 q or p = q 9. The answer to the First part of this question is the formula for the number of combinations of n things taken r at a time, viz., I r | H— r Second part In sets of 2 each, and of 8 each, the number would be the same,... | |
 | Edward John Hamilton - Psychology - 1883 - 740 pages
...that s=n—r, the expression becomes, '""^".l!'!''.....'.'.'.'.'?" 1 "'- But this is th » general formula for the number of combinations of n things taken r at a time. In the same manner, cancelling the first series in the denominator, we obtain a similar expression... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...Assuming the formula for the number of arrangements of « different things taken r together, prove the formula for the number of combinations of n things taken r together. A man has 10 friends : how many different parties could he make by inviting them six together?... | |
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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. 
