Calendar: 1877-1878 Page 590

588 GENERAL LITERATURE AND SCIENCE Prove that the sum of the first τ -f1 coefficients of the expansion of η lיי χ μ Γ The arithmetical mean of η positive quantities is not less than their geometrical mean Shew that be ac ab being positive Find the number of permutations of things taken together If nP denote the number of permutations of η things taken all together in which group of specified things occurs together prove that χ nPl ZFיי י ηΐ fi If η be an interger so is "S -J- IuL 4- 52 י υ י Enunciate and prove Fermat's theorem If be prime number -ני -f -1 1- is divisible by The probability of an event happening in one trial being given determine the probability of its happening times exactly in trials times at least in trials bag contains π coins which may be sovereigns or shillings Two are drawn out and found to be sovereigns Determine the probability that all the rest are sovereigns If two roots of the equation ax3 3bx 3cx are equal prove that ac IP bd c2 ad bef 10 Enunciate and prove Descartes' rule of signs