 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...remember that the number of factors is equal to the number of letters taken in a set. 338. To find the number of permutations of n things taken all at a time, put r = n in formula (A) ; the result will be ra(n— !)(»— 2)....l. (B) That is, The number of... | |
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...remember that the number of factors is equal to the number of letters taken iu a set. 338. To find the number of permutations of n things taken all at a time, put r — n in formula (A) ; the result will be n(n— l)(n— 2).... L (B) That is, The number of... | |
 | George Shoobridge Carr - Mathematics - 1880
...Harmonic do. = T. a+b The three means are in continued proportion. PERMUTATIONS AND COMBINATIONS. 94 The number of permutations of n things taken all at a time = n (n—l) (n— 2) ... 3 . 2 . l = \n_ or пм. PROOF BY INDUCTION. — Assume the formula to be... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...Harmonic do. = r. a + b The three means are in continued proportion. PERMUTATIONS AND COMBINATIONS. 94 The number of permutations of n things taken all at a time = n (n— 1) (n— 2) ...3.2.1 = ni or n(B). PROOF BY INDUCTION. — Assume the formula to be true... | |
 | Edward Albert Bowser - Algebra - 1888 - 868 pages
.... (1) If all the letters are taken together, r = n, and (1) becomes n(nl)(n-2) 3-2.1. . .(2) Hence, the number of permutations of n things taken all at a time is equal to the product of the natural numbers from 1 up to n. It is usual to denote this product by... | |
 | James Morford Taylor - Algebra - 1889 - 400 pages
...letters in the word courage, so that the consonants may occupy even places? • . L 347. IfN denote the number of permutations of n things taken all at a time, of which r things are alike, s others alike, and t others alike ; then _ \from this single permutation,... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...Therefore the number of permutations of n tilings taken r at a time is n(n- 1) (n-2) ...... (nr + 1). COR. The number of permutations of n things taken all at a time is n (n - 1) (n - 2) ...... to n factors, or n(nl)(n-2) ...... 3.2.1. It is usual to denote this product... | |
 | Matthew Scoby McCurdy - 1894 - 240 pages
...Democrats ? 13. How many different numbers of 5 figures each can be formed from the 10 digits ? 14. The number of permutations of n things taken all at a time is 5040 : find the value of n. 15. Out of 8 letters, x of which are alike, 336 words can be formed... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...Therefore the number of permutations of n things taken r at a time is »(я-1)(л-2) (nr + 1). Сок. The number of permutations of n things taken all at a time is n (n—l) (та — 2) to n factors, or я(п-1)(п-2) 3.2.1. It is usual to denote this product... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 552 pages
...Therefore the number of permutations of n things taken r at a time is n(n - T)(n - 2)..-(n -r + 1). Сов. The number of permutations of n things taken all at a time is n(n — T)(n — 2)"- to n factors, or n(nl)(n — 2)—3-2-l. It is usual to denote this product... | |
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We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike. 
