...things taken 5 at a time is to the number where 3 are taken at a time as 1 8 is to 5 ; find и. 759. The number of permutations of n things taken r at a time is equal to 10 times the number taken (1 — 1) at a time: and the number of combinations of n things...

...a time. The number of combinations of n things taken r at a time is n(nl)(n-2) (nr + l) " ~E ' For the number of permutations of n things taken r at a time is n(n — 1) (n — 2) (и — r + 1) by Art. 490; and each combination produces |_r permutations, by...

...a time. The number of combinations of n things taken r at a time is n(nl)(n-2) (n-r+ 1) ~Tr " ' For the number of permutations of n things taken r at a time is n(n— l)(n — 2) (n — r+l), by Art. 490; and each combination produces \r_ permutations, by Art....

...years will £P double itself at 6 per cent. per ann. Compound interest payable half-yearly 1 APPENDIX. 475. The following is another method of proving the...reference is made in the note on page 289. To prove that tfie number of permutations of n things talcen r at a time is n.(n- 1) (n - r+1). Let there be n things...

...years will £P double itself at 6 per cent. per ann. Compound interest payable half-yearly ? APPENDIX. 475. The following is another method of proving the...reference is made in the note on page 289. To prove thai the number of permutations of n things taken r at a time is n.(n — 1) (n — r + 1). Let there...

...years will £P double itself at 6 per cent. per ann. Compound interest payable half-yearly ? APPENDIX. 475. The following is another method of proving the...289. To prove that the number of permutations of n thing» taken rata time is n.(nl) (nr + 1). Let there be n things a,b,c,d If и things be taken 1 at...

...though different permutations, form the same combination, so also do ae and ca, and be and cb. 417. The number of permutations of n things taken r at a time is n(n- l)(n- 2) (n- r + 1). Let there be n letters а, b, с, d, ; we shall first find the number of...

...of combinations ofn. thingt taken r . n(nl)fn-2)...(nr + l) at a lime is -* ' A — - -. TA ~ 17 For the number of permutations of n things taken r at a time is n (n — l)(n— 2)...(n-r+l)by Art. 417; and each combination produces r permutations by Art. 420; hence...

...years will £P double itself at 6 per cent. per ann. compound interest payable half-yearly ? APPENDIX. 475. THE following is another method of proving the...theorem in Permutations, to which reference is made iu the note on page 289. To prove that the number of permutations of n things taken r at a time is...

...6. In how many years will ¿£1000 amount to ¿£1800 at 5 per cent. compound interest 1 APPENDIX. 475. THE following is another method of proving the...taken r at a time is n. (n-1) (n — r+1). Let there be n things a,b,c,d If и things be taken 1 at a time, the number of permutations is of course n. Now...