...always the same. 7. (a) Distinguish between a permutation and a combination. (6) Find the expression for the number of permutations of n different things taken r at a time, where r is any integer not greater than n. (c) At an election there are 5 candidates and 3 members...

...arithmetical progression so are a2 — be, V* — ca, c" — ab. 3. State and prove the formula for the number of permutations of n different things taken r at a time. Prove that — P = n P nr n—lr—l 4. State and prove the hinomial theorem for a positive integral...

...more than 2 lines intersecting in the same point, how many points of intersection will there be ? 103. The number of permutations of n different things, taken r at a time, when each of the n things can be repeated, ¡3 nr. After the first place has been filled by one of...

...only one combination of any number of things taken all at a time. 601. Notation. — The symbol for the number of permutations of n different things, taken r at a time, is P?; of n different things, taken и at a time, or all together, is P". Instead of P£, sometimes "P.,...

...this number is equal to n ! by 154. Therefore x-klllml=n\, i »! 1111(1 в"ШТИГ1' 166. Theorem. The number of permutations of n different things taken r at a time, when any one of them can occur 'once, twice, and so on, up to r times in each permutation, is equal...

...x 3 x 2 x 1 ; [и = Ь2-3... (и - 2) (и- 1)n, or н(и- 1) (n - 2) (ra-3) — 3-2-1. 603. To find the number of permutations of n different things taken r at a time. Since the permutations of a, b, and c, taken 2 at a time, are ab and ac, ba and 6e, ca and cb, formed...

...OiC+X^ Prove that the pth., i/tii., and rth. terms of a GP ate in GP, if p, q, r are in AP 8. Prove that the number of permutations of n different things taken r at a time is ii (n - I) (n - 2). ...(«- r 4 1). One family consists of 4 sons and 3 daughters, and another family...

...number of permutations of n things taken r at a time. The symbol „Pr is used to represent this number. The number of permutations of n different things taken r at a time is The number „Pr required is the same as the number of ways of filling r different positions with n...

...n natural numbers. 7 (&) Sum to n terms the following series: 1. 2. 3+2. 3. 4+3. 4. 5+ 7. (a) Find the number of permutations of n different things taken r at a time where r is any integer not greater .than n. (b) In how many ways can 7 Englishmen and 7 Americans sit...

...— l)(n — 2) ••• to r factors, and the rth factor is n — (r — 1) or n — r+1. Therefore the number of permutations of n different things taken r at a time is (1) nPr = n(nl)(n-2)...(nr + l). COROLLARY. If r = n, we have (2) nPM = ;i (n - l)(n - 2) - 3 • 2...