Menu Close

Category: Permutation and Combination

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…

Find-the-coefficient-of-x-50-in-the-expression-1-x-1000-2x-1-x-999-3x-2-1-x-998-1001x-1000-

Question Number 139332 by bemath last updated on 26/Apr/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{50}} \:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{1000}} \:+\mathrm{2x}\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{999}} + \\ $$$$\mathrm{3x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{998}} +…+\mathrm{1001x}^{\mathrm{1000}} \\ $$ Answered by mr W…

1-1-x-n-n-0-n-1-x-n-2-x-2-n-3-x-3-

Question Number 139286 by qaz last updated on 25/Apr/21 $$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}} }=\left(\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\right)+\left(\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\right){x}+\left(\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\right){x}^{\mathrm{2}} +\left(\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\right){x}^{\mathrm{3}} +… \\ $$ Commented by mr W last updated on 25/Apr/21 $${wrong}! \\…