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Category: Permutation and Combination

The-first-3-runners-in-100m-race-were-clocked-9-5s-10s-10-5s-respectively-How-far-is-the-first-from-the-third-runners-when-the-first-runner-reached-the-finished-line-

Question Number 10029 by Tawakalitu ayo mi last updated on 21/Jan/17 $$\mathrm{The}\:\mathrm{first}\:\mathrm{3}\:\mathrm{runners}\:\mathrm{in}\:\mathrm{100m}\:\mathrm{race}\:\mathrm{were}\:\mathrm{clocked} \\ $$$$\mathrm{9}.\mathrm{5s},\:\mathrm{10s},\:\mathrm{10}.\mathrm{5s}\:\mathrm{respectively}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{first}\:\mathrm{from}\:\mathrm{the}\:\mathrm{third}\:\mathrm{runners}\:\mathrm{when}\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{runner}\:\mathrm{reached}\:\mathrm{the}\:\mathrm{finished}\:\mathrm{line}. \\ $$ Commented by mrW1 last updated…

Find-the-coefficient-of-the-term-independent-of-x-in-the-expansion-of-x-1-x-2-3-x-1-3-1-x-1-x-x-1-2-10-

Question Number 9747 by tawakalitu last updated on 30/Dec/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{term}\:\mathrm{independent} \\ $$$$\mathrm{of}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\frac{\mathrm{x}\:+\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}/\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{1}/\mathrm{3}} \:+\:\mathrm{1}}\:−\:\frac{\mathrm{x}\:−\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{x}^{\mathrm{1}/\mathrm{2}} }\right)^{\mathrm{10}} \\ $$ Answered by sandy_suhendra last updated on…

There-are-6-girls-and-four-boys-in-a-class-3-students-are-choosen-at-random-so-as-to-be-awarded-a-scholaship-In-how-many-ways-can-this-be-done-if-atlease-1-boy-and-1-girl-must-in-the-selection-

Question Number 75180 by Rio Michael last updated on 08/Dec/19 $${There}\:{are}\:\mathrm{6}\:{girls}\:{and}\:{four}\:{boys}\:{in}\:{a}\:{class}. \\ $$$$\mathrm{3}\:{students}\:{are}\:{choosen}\:{at}\:{random}\:{so}\:{as}\:{to}\:{be} \\ $$$${awarded}\:{a}\:{scholaship}.{In}\:{how}\:{many}\:{ways}\:{can} \\ $$$${this}\:{be}\:{done}\:{if}\:{atlease}\:\mathrm{1}\:{boy}\:{and}\:\mathrm{1}\:{girl}\:{must} \\ $$$${in}\:{the}\:{selection} \\ $$$$ \\ $$ Commented by…

Question-75122

Question Number 75122 by chess1 last updated on 07/Dec/19 Commented by JDamian last updated on 07/Dec/19 $${Open}\:{this}\:{app},\:{tap}\:{on}\:\boldsymbol{\mathrm{Study}}\:>\:\boldsymbol{\mathrm{Sequence}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{Series}}\:{and}\:{look}\:{for}\:\boldsymbol{\mathrm{Sum}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{terms}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{G}}.\boldsymbol{\mathrm{P}}. \\ $$ Commented by…

If-n-is-positive-integer-prove-that-the-cofficient-of-x-2-and-x-3-in-the-expansion-of-x-2-2x-2-n-are-2-n-1-n-2-and-2-n-1-n-n-1-1-3-

Question Number 9573 by lepan last updated on 17/Dec/16 $${If}\:{n}\:{is}\:{positive}\:{integer}\:{prove}\:{that}\: \\ $$$${the}\:{cofficient}\:{of}\:{x}^{\mathrm{2}\:} {and}\:{x}^{\mathrm{3}} \:{in}\:{the}\: \\ $$$${expansion}\:{of}\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{{n}} \:{are}\:\mathrm{2}^{{n}−\mathrm{1}} .{n}^{\mathrm{2}} \\ $$$${and}\:\mathrm{2}^{{n}−\mathrm{1}} {n}\left({n}−\mathrm{1}\right)\frac{\mathrm{1}}{\mathrm{3}}. \\ $$ Commented…