Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 93764 by DuDono last updated on 14/May/20

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

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

Commented by mr W last updated on 14/May/20

do you mean Σ_(x=0) ^n ((n!)/(x!(n−x)!)) ? Σ_(x=0) ^n ((n!)/(x!(n−x)!))=Σ_(x=0) ^n C_x ^n =(1+1)^n =2^n

$${do}\:{you}\:{mean}\:\underset{{x}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{n}!}{{x}!\left({n}−{x}\right)!}\:? \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{{n}!}{{x}!\left({n}−{x}\right)!}=\underset{{x}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{{x}} ^{{n}} =\left(\mathrm{1}+\mathrm{1}\right)^{{n}} =\mathrm{2}^{{n}} \\ $$

Commented by DuDono last updated on 14/May/20

no, x must appear somewhere. You can imagine it as a function if you want

$$ \\ $$$$\mathrm{no},\:{x}\:\mathrm{must}\:\mathrm{appear}\:\mathrm{somewhere}.\:\mathrm{You}\: \\ $$$$\mathrm{can}\:\mathrm{imagine}\:\mathrm{it}\:\mathrm{as}\:\mathrm{a}\:\mathrm{function}\:\mathrm{if}\:\mathrm{you}\:\mathrm{want} \\ $$

Commented by mr W last updated on 14/May/20

THEN YOUR QUESTION IS WRONG! in Σ_(x=0) ^k a_x the symbol x is just a counter, you can replace it with any symbol. Σ_(x=0) ^k a_x =Σ_(y=0) ^k a_y = Σ_(ψ=0) ^k a_ψ . Σ_(x=0) ^k ((n!)/(x!(n−x)!)) can be a function of n or a function of k, but never a function of x. this is such basic in mathematics as 1+1=2.

$${THEN}\:{YOUR}\:{QUESTION}\:{IS} \\ $$$${WRONG}!\: \\ $$$${in}\:\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\:{a}_{{x}} \:{the}\:{symbol}\:{x}\:{is}\:{just}\:{a}\:{counter}, \\ $$$${you}\:{can}\:{replace}\:{it}\:{with}\:{any}\:{symbol}. \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\:{a}_{{x}} =\underset{{y}=\mathrm{0}} {\overset{{k}} {\sum}}\:{a}_{{y}} =\:\underset{\psi=\mathrm{0}} {\overset{{k}} {\sum}}\:{a}_{\psi} . \\ $$$$\underset{{x}=\mathrm{0}} {\overset{{k}} {\sum}}\:\frac{{n}!}{{x}!\left({n}−{x}\right)!}\:{can}\:{be}\:{a}\:{function}\:{of}\:{n} \\ $$$${or}\:{a}\:{function}\:{of}\:{k},\:{but}\:{never}\:{a} \\ $$$${function}\:{of}\:{x}.\:{this}\:{is}\:{such}\:{basic}\:{in} \\ $$$${mathematics}\:{as}\:\mathrm{1}+\mathrm{1}=\mathrm{2}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com