Permutation and Combination – Page 10

Sum-the-series-n-C-1-n-C-0-2-2-n-C-2-n-C-1-3-n-C-3-n-C-2-2-n-terms-

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Question Number 59625 by Tawa1 last updated on 12/May/19 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\:\:\:\left(\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{0}} }\right)^{\mathrm{2}} \:+\:\left(\mathrm{2}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }\right)\:+\:\left(\mathrm{3}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{3}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:….\:\:\boldsymbol{\mathrm{n}}\:\mathrm{terms} \…

let-S-a-b-c-d-e-f-if-we-take-any-subset-S-same-subset-is-allowed-it-also-can-be-S-which-will-form-S-if-we-join-them-order-of-operation-does-not-matter-a-b-c-d-d-e-f-is-the-same-as-

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Question Number 190602 by uchihayahia last updated on 07/Apr/23 $l e t S = {a, b, c, d, e, f}$ $i f w e t a k e a n y s u b s e t S (s a m e s u b s e t i s a l l o w e d),$ $i t a l s o c a n b e S, w h i c h w i l l f o r m S i f w e j o i n t h e m,$ $o r d e r o f o p e r a t i o n d o e s n o t m a t t e r$ $({a, b, c, d}, {d, e, f}) i s t h e s a m e a s$ $$\:\left(\left\{{d},{e},{f}\right\},\left\{{a},{b},{c},{d}\right\}\right) \…

The-number-of-ways-arrangements-of-the-word-MASKARA-with-exactly-2-A-s-are-adjacent-

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Question Number 124916 by liberty last updated on 07/Dec/20 $T h e n u m b e r o f w a y s a r r a n g e m e n t s$ $o f t h e w o r d^{'} {M A S K A R A}^{'} w i t h e x a c t l y$ $2 A^{'} s a r e a d j a c e n t ? ?$ Answered by mr W last updated on 07/Dec/20 $$\_\mathrm{M\_S\_K\_R\_}…

20-students-should-stand-in-5-different-rows-each-row-should-have-at-least-2-students-in-how-many-ways-can-you-arrange-them-

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Question Number 124878 by mr W last updated on 06/Dec/20 $20 s t u d e n t s s h o u l d s t a n d i n 5$ $d i f f e r e n t r o w s . e a c h r o w s h o u l d h a v e$ $a t l e a s t 2 s t u d e n t s . i n h o w m a n y w a y s$ $c a n y o u a r r a n g e t h e m ?$ Answered by liberty last updated on…

How-many-ways-are-there-to-arrange-the-letters-of-the-word-VISITING-if-no-two-I-s-are-adjacent-

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Question Number 124826 by bramlexs22 last updated on 06/Dec/20 $H o w m a n y w a y s a r e t h e r e t o a r r a n g e$ $t h e l e t t e r s o f t h e w o r d^{'} {V I S I T I N G}^{'}$ $i f n o t w o I^{'} s a r e a d j a c e n t ?$ Answered by mr W last updated on 06/Dec/20 $${Method}\:{I}…

How-many-ways-are-there-to-arrange-the-letters-of-the-word-ALAMATAR-if-no-two-A-s-are-adjacent-

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Question Number 124829 by bramlexs22 last updated on 06/Dec/20 $H o w m a n y w a y s a r e t h e r e t o a r r a n g e$ $t h e l e t t e r s o f t h e w o r d^{'} {A L A M A T A R}^{'} i f$ $n o t w o A^{'} s a r e a d j a c e n t ?$ Answered by mr W last updated on 06/Dec/20 $${to}\:{arrange}\:{at}\:{first}\:{the}\:{four}\:{letters}…

how-is-solution-lim-x-sinpi-sin-pi-2-sinx-

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Question Number 190347 by mustafazaheen last updated on 01/Apr/23 $h o w i s s o l u t i o n$ $\lim_{x \to \sin π} \frac{\sin \frac{π}{2}}{\sin x} = ?$ Answered by JDamian last updated on 01/Apr/23 $${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\begin{cases}{+\infty\:\:\:{x}\rightarrow\mathrm{0}^{+} }\{−\infty\:\:{x}\rightarrow\mathrm{0}^{−}…

Question-124806

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Question Number 124806 by bramlexs22 last updated on 06/Dec/20 Answered by mr W last updated on 06/Dec/20 $(i)$ $6 = 1 + 5 = 2 + 4 = 3 + 3$ $$\Rightarrow{C}_{\mathrm{1}} ^{\mathrm{6}} ×\mathrm{4}!+{C}_{\mathrm{2}} ^{\mathrm{6}}…

f-1-3-R-f-x-1-x-A-1-1-B-1-1-3-B-b-1-b-b-1-Find-i-equation-of-line-AB-ii-equation-of-tangent-T-to-C-f-at-point-with-x-1-b-2-iii-Study-relative-positions-of-L-

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Question Number 190260 by alcohol last updated on 30/Mar/23 $f : [1, 3] \to R, f (x) = \frac{1}{x}$ $A (1, 1)$ $B (1, \frac{1}{3})$ $B^{'} (b, \frac{1}{b}), b ⩾ 1$ $F i n d$ $i . e q u a t i o n o f l i n e {A B}^{'}$ $i i . e q u a t i o n o f t a n g e n t T^{'} t o C_{f} a t p o i n t$ $${with}\:{x}\:=\:\frac{\mathrm{1}\:+\:{b}}{\mathrm{2}}…

In-how-many-ways-can-5-boys-and-3-girls-be-seated-around-a-table-if-i-boy-B-3-and-G-2-are-not-adjacent-ii-no-girls-are-adjacent-

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Question Number 124712 by benjo_mathlover last updated on 05/Dec/20 $I n h o w m a n y w a y s c a n 5 b o y s a n d 3 g i r l s$ $b e s e a t e d a r o u n d a t a b l e i f$ $(i) b o y B_{3} a n d G_{2} a r e n o t a d j a c e n t$ $(i i) n o g i r l s a r e a d j a c e n t$ Answered by liberty last updated…

Category: Permutation and Combination