...COMBINATIONS. 487. The different orders in which any things can be arranged are called their permutations. Thus the permutations of the letters a, b, c, taken two at a time are ab, ba, ac, ca, be, cb. 488. The combinations of things are the different collections that can be formed...

...COMBINATIONS. 487. The different orders in which any things can be arranged are called their permutations. Thus the permutations of the letters a, b, c, taken two at a time are db, ba, ac, ca, be, cb. 488. The combinations of things are the different collections that can be formed...

...of any things, taking the whole or a certain number of them together, are called their permutations. Thus the permutations of the letters a, b, c, taken two at a time, or two and two together, are ab, ba, fie, еa, be, cb ; taken three together, the permutations are...

...things are placed, the same number of elements entering into all the results. Thus, the combinations of the letters, a, b, c, taken two at a time, are ab, ас, be. It will be observed that if the letters be regarded as factors, the combinations which may be formed...

...ca ; be, cb ; and taken three at a time, are ale, acb; bac, be a; cab, cba. Thus, the combinations of the letters a, b, c, taken two at a time, are ab, ac, be, ab and ba, though different permutations, forming the same combination. 350. To find the number...

...things are placed, the same number of elements entering into all the results. Thus, the combinations of the letters, a, b, c, taken two at a time, are ob, ас, be. It will be observed that if the letters be regarded as factors, the combinations which...

...COMBINATIONS. 487. The different orders in which any things can be arranged are called their permutations. Thus the permutations of the letters a, b, c, taken two at a time are ab, ba, ac, ca, bo, cb. 488. The combinations of things are the different collections that can be formed...

...formed out of them, without regarding the order in which the things are placed. Thus the combinations of the letters a, b, c, taken two at a time are ab, ас, be; ab and ba though different permutcuwM forming the same combination. 489. "We may observe that a...

...a time ; but in any proposed system, the different results must contain the same number of things. Thus, the permutations of the letters, a, b, c, taken two at a time, are аЪ, Ъа, ас, са, Ъс, cb. The permutations of the same letters taken all al a time, are cab,...

...COMBINATIONS. 487. The different orders in which any things can be arranged are called their permutations. Thus the permutations of the letters a, b, c, taken two at a лте are ab, Ъа, ас, ca, be, cb. 488. The combinations of things are the different collections...