...r factors, that is, n(n — 1) (n — 2) [n - (r — 1)], or n (n — 1) (n — 2) (n — r+1). For the first place can be filled in n ways, the second in n - 1 ways, the third place in n - 2 ways, and the rth place in n - (r - 1) ways. (1) A shelf contains 4 English books, 5...

...factors, that is, n(n — 1) (n — 2) [n — (r — 1)], or и(и — 1)(» — 2) (n — r + 1). • For the first place can be filled in n ways, the second in TÍ - 1 ways, the third place in n - 2 ways, and the rth place in n - (r - 1) ways. (1) A shelf contains...

...place may be filled ¡nn ways, then the second place in n — 1 ways, then the third place in и — 2 ways, and so on to the last place, which can be filled in only 1 way. Hence (Rule II.) the whole number of arrangements is the continued product of all these...

...the first place can be filled in n ways, then the second place in n — 1 ways, then the third place in n — 2 ways, and so on to the last place, which can be filled in only 1 way. Hence (§ 298) the whole number of arrangements is the continued product of all these numbers,...

...any one of the n things, or in n ways ; the second by any one oí the remaining n — 1 things, or in n — 1 ways ; the third in n — 2 ways, and so on until the last place is reached, which must be filled by the only one remaining. Therefore, the number...

...the first place can be filled in n ways, then the second place in n — 1 ways, then the third place in n — 2 ways, and so on to the last place, which can be filled in only 1 way. Hence (§ 376) the whole number of arrangements is the continued product of all these numbers,...

...the first place can be filled in n ways, then the second place in и — 1 ways, then the third place in n — 2 ways, and so on to the last place, which can be filled in only 1 way. Hence (§ 23), the whole number of arrangements is n (n - 1) (n - 2) (n - 3) 3X2X1. For...

...place can be filled in n ways, then the second place in n — 1 ways, then the third place in я — 2 ways, and so on, to the last place, which can be filled in only 1 way. Hence (§ 337), the whole number of arrangements is the continued product, n(n - 1) (и...

...the first place can be filled in n ways, then the second place in n - 1 ways, then the third place in n - 2 ways, and so on, to the last place, which can be filled in only 1 way. Hence (p. 392, § 479), the whole number of permutations is the continued product of these...

...the number of different ways we can select r balls from n balls. As before, we can select the first in n ways, the second in n — 1 ways, the third in n — 2 ways, and finally the rth in n — r + 1 ways. We have then n(n — l)(n — 2) . . . (n — r + 1) ways, not...