# Calendar: 1878-1879 Page 594

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592 GENERAL LITERATURE AND SCIENCE XXI -aigtbra anil 3Ti cov1 of Equations If fl3 ala2 la3 Vs then Oj a2 a3 Prove the binomial theorem for fractional and negative indices Prove that -1 tl The probability of an event happening in one trial being known find the probability of its happening at least times in η trials If out of 10 ships return safe to port what is the chance that of ships expected at least will arrive Ρ Find numbers in geometrical progression so that their sum may be 15 and the sum of their squares 85 Find the number of different combinations of η things taken ρ together Prove that the number of ways in which ρ positive signs and negative signs may be placed in row so that no two negative signs may be together is equal to the number of combinations of ρ things taken together If be in geometrical progression and loge logs 10ga in arithmetical progression the common difference of this pro- gression is Find the general terms of the expansion of the multi- liomial ---- and shew that the co-efficient of any term where one and only one of the quantities av a2 a3 appears twice is £ Shew that in scale of notation of which the radix is the sum of the digits of any whole number divided by will leave the same remainder as the whole number divided by

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