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Permutation and CombinationQuestion and Answers: Page 15

Question Number 100444    Answers: 4   Comments: 0

Find the number of five−digit numbers containing exactly three different digits? Examples: 12312, 12224

$${Find}\:{the}\:{number}\:{of}\:{five}−{digit}\:{numbers} \\ $$$${containing}\:{exactly}\:{three}\:{different} \\ $$$${digits}?\:{Examples}:\:\mathrm{12312},\:\mathrm{12224} \\ $$

Question Number 99985    Answers: 0   Comments: 0

A certain wire has length 4.5 cm and mass 12.3 g, with an electrical resistance of 1.1 mΩ. this wire falls through a horizontal magnetic field with flux density of 0.35 T. As his wire falls its ends slide smoothly between two rails connected by a wire with negligible internal resistance. Calculate the magnitude of the terminal energy resistance, neglecting the resistance of the rails.

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$

Question Number 99905    Answers: 0   Comments: 5

Question Number 99194    Answers: 1   Comments: 0

Question Number 98405    Answers: 1   Comments: 0

Question Number 98406    Answers: 0   Comments: 0

NB:P(E) means a set of all part of E

$$\boldsymbol{{NB}}:\boldsymbol{\mathcal{P}}\left(\boldsymbol{\mathrm{E}}\right)\:\mathrm{means}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{part}\:\mathrm{of}\:\boldsymbol{\mathrm{E}} \\ $$

Question Number 98030    Answers: 0   Comments: 1

Question Number 98027    Answers: 0   Comments: 1

One card is randomly selected from a pack of 52 playing cards. Determine the probability that is a picture card.

$$\mathrm{One}\:\mathrm{card}\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{selected} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{pack}\:\mathrm{of}\:\mathrm{52}\:\mathrm{playing}\:\mathrm{cards}. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{picture}\:\mathrm{card}.\: \\ $$

Question Number 97600    Answers: 1   Comments: 0

Question Number 97492    Answers: 2   Comments: 0

Question Number 97045    Answers: 0   Comments: 4

a committee consisting of 5 men & 4 women is to be chosen from 8 men & 4 women. If one man & one woman are husband & wife , how many ways can the committee be chosen if only one of the husband & wife must be chosen ?

$$\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of} \\ $$$$\mathrm{5}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{chosen}\:\mathrm{from}\:\mathrm{8}\:\mathrm{men}\:\&\:\mathrm{4}\:\mathrm{women}. \\ $$$$\mathrm{If}\:\mathrm{one}\:\mathrm{man}\:\&\:\mathrm{one}\:\mathrm{woman}\:\mathrm{are}\:\mathrm{husband}\: \\ $$$$\&\:\mathrm{wife}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\: \\ $$$$\mathrm{the}\:\mathrm{committee}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{if} \\ $$$$\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{husband}\:\&\:\mathrm{wife} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{chosen}\:? \\ $$

Question Number 96815    Answers: 1   Comments: 0

In how many ways can 3 boys and 3 girls be sitted in a line?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{be} \\ $$$$\mathrm{sitted}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}? \\ $$

Question Number 96276    Answers: 0   Comments: 5

Question Number 95912    Answers: 0   Comments: 2

(((2n)),(n) ) = 20 find n?

$$\begin{pmatrix}{\mathrm{2n}}\\{\mathrm{n}}\end{pmatrix}\:=\:\mathrm{20}\: \\ $$$$\mathrm{find}\:\mathrm{n}? \\ $$

Question Number 95888    Answers: 1   Comments: 0

(1−2x)^5 (2+x)^6 = a+bx+cx^2 +dx^3 +... find : a,b,c and d

$$\left(\mathrm{1}−\mathrm{2x}\right)^{\mathrm{5}} \left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{6}} =\:\mathrm{a}+\mathrm{bx}+\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}^{\mathrm{3}} +... \\ $$$$\mathrm{find}\::\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\: \\ $$

Question Number 95723    Answers: 3   Comments: 1

Question Number 95578    Answers: 0   Comments: 8

Question Number 95436    Answers: 1   Comments: 0

∫((x^4 dx)/(x^8 +x^4 +1))

$$\int\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\mathrm{x}^{\mathrm{8}} +\mathrm{x}^{\mathrm{4}} +\mathrm{1}} \\ $$

Question Number 94397    Answers: 1   Comments: 0

Question Number 94352    Answers: 0   Comments: 4

Question Number 93764    Answers: 0   Comments: 3

define Σ_(x=0) ^k ((n!)/(x!(n−x)!)) without Σ symbol

$$\mathrm{define} \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\frac{{n}!}{{x}!\left({n}−{x}\right)!} \\ $$$$\mathrm{without}\:\Sigma\:\mathrm{symbol} \\ $$

Question Number 93450    Answers: 2   Comments: 0

what is the value of coefficient of x^9 in expansion (1+x)(1+x^2 ) (1+x^3 )(1+x^4 )×...×(1+x^(100) ) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{coefficient} \\ $$$$\mathrm{of}\:\mathrm{x}^{\mathrm{9}} \:\mathrm{in}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)×...×\left(\mathrm{1}+\mathrm{x}^{\mathrm{100}} \right)\:? \\ $$

Question Number 92923    Answers: 1   Comments: 0

Solve 1+(x/(2!))+(x^2 /(4!))+(x^3 /(6!))+∙∙∙ =0

$$\mathrm{Solve} \\ $$$$\mathrm{1}+\frac{\mathrm{x}}{\mathrm{2}!}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}!}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}!}+\centerdot\centerdot\centerdot\:=\mathrm{0} \\ $$

Question Number 92319    Answers: 0   Comments: 3

log _9 (x+(7/2)).log _(3/4) (x^2 ) ≥ log _(3/4) (x+(7/2))

$$\mathrm{log}\:_{\mathrm{9}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right).\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}^{\mathrm{2}} \right)\:\geqslant\: \\ $$$$\mathrm{log}\:_{\mathrm{3}/\mathrm{4}} \left(\mathrm{x}+\frac{\mathrm{7}}{\mathrm{2}}\right)\: \\ $$

Question Number 91230    Answers: 2   Comments: 0

Σ_(j=o) ^m ^a C_j ^b C_(m−j) = ^(a+b) C_m solve this problem

$$\underset{{j}={o}} {\overset{{m}} {\sum}}\:\:\overset{{a}} {\:}{C}_{{j}} \:\overset{{b}} {\:}{C}_{{m}−{j}} \:\:=\:\overset{{a}+{b}} {\:}{C}_{{m}} \\ $$$${solve}\:{this}\:{problem} \\ $$

Question Number 90531    Answers: 0   Comments: 2

Please help me to find the value of ′n′ C_8 ^(n+3) =C_(20) ^(n+3)

$${Please}\:{help}\:{me}\:{to}\:{find}\:{the}\:{value} \\ $$$${of}\:\:\:'{n}' \\ $$$${C}_{\mathrm{8}} ^{{n}+\mathrm{3}} ={C}_{\mathrm{20}} ^{{n}+\mathrm{3}} \\ $$

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