...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...

...• 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...

...a time is n(n — l)(n — 2)"-[n — (r — 1)] ; that is, .J>- = n(nl)(n-2)...(nr + l). (1) Note. The number of permutations of n different things taken r at a time, is usually denoted by the symbol nP-. 543. If all the letters are taken together, r = n, and formula (1)...

...letters taken two at a time is equal to n(n-1). 542. We will now discuss the general case. To find the number of permutations of n different things taken r at a time. Consider the letters .., a.. Take any permutation containing r letters, for example the one consisting...

...= n(n—l) (n - 2) (n - 3) ; P6 = n(nl)(n — 2) (n - :'.) (n - 4) ; and so on. Hence, in general, The number of permutations of n different things, taken r at a time, is n (n - 1) (n - 2) (n — 3) ••• * [n - (r - 1)] ; that is, .Рг = я(я-1)(и-2)(я-3)(п-4)...

...of permutations of n different things taken r at a time is denoted by the symbol „Pr. 338. To find the number of permutations of n different things taken r at a time, where r is any integer not greater than n. Let the different things be represented by the letters a,...