...r(r—Y)(r—V) . . . . 1. Hence, we have ^ _ «(*r( That is, The number of combinations of n Utters taken т at a time, is equal to the continued product of the natural numbers from n down to n — rj-1 inclusive, divided by the continued product of the natural numbers from r doten...

...: ..... ,.(,— l)(r-2)....l • ( f' } That is, The number of combination» of n letters taken т at a time, is equal to the continued product of the natural numbers from n down to n — г-{-1 inclusive, divided by the continued product of the natural numbers from r down...

...the same letters taken one at a time are a, 6, c. 344. The number of permutations ofn things taken m at a time is equal to the continued product of the natural series of numbers from n down to n—m + 1. Suppose the things to be n letters, a, &, c, d The number...

...and JR taken two at a time are six in number, thus : P,Q; P,R; Q,P; Q,R; R, P ; R, Q. 404. To find the number of permutations of n different things taken r at a time. Let a,b,c,d... stand for n different things. First to find the number of permutations of the n things...

...being performable in an ways, the whole number of ways of performing all the compound processes is II. The number of permutations of n different things taken r at a time III. The number of permutations of n different things taken r at a time, when each may be repeated...

...the same letters taken one at a time are a, b, c. 344. The number of permutations ofn things taken m at a time is equal to the continued product of the natural series of numbers •from, n down to n—m + l. Suppose the things to be n letters, a,b,c,d The number...

...• arrangements that can be made of them, without reference to the order in which they appear. 77. The number of permutations of n different things taken r at a time =n(n—\)(n—2) .... (n— r+i). 78. The number of permutations of n different things taken all together...

...a, b, c, d; the permutations two at a time are ab, ba, ac, ca, ad, da, be, cb, bd, db, cd, and dc. The number of permutations of n different things taken r at a time is denoted by the symbol %РГ 237. To find the number of permutations of n different things taken r at...

...b, c, taken three at a time, form but one combination. 180. The Number of Permutations. — To find the number of permutations of n different things, taken r at a time. Let the different things be represented by n letters, a, 6, c, Set a aside ; write down the other n...

...be taken one at a time in n separate ways. 369. Number of permutations of n things taken r together. The number of permutations of n different things taken r at a time is given by the formula BPr = n(«-l) (nr + 1). Let us denote the things by the letters a,b,c, .... Suppose...