Answer
414.6k+ views
Hint: To calculate the value of $x + y$ we can compare this given equation with the standard equation of combination in terms of $n$ and $r$, then by comparing we will get the respective values for $x$ and $y$ and then finally by substituting those values of $x$ and $y$ in $x + y$ we will get the value of $x + y$.
Formula used: ${}^n{C_r}\, = \,{}^n{C_{n - r}}$ where $n$ is total items and $r$ is selected number of items.
Complete step-by-step answer:
According to question we are given,
${}^n{C_x}\, = \,{}^n{C_y}$ and we have to find the value of $x + y$
As we know the property of Combination which says ${}^n{C_r}\, = \,{}^n{C_{n - r}}$
So, comparing both of the equations that is,
${}^n{C_x}\, = \,{}^n{C_y}\,$ and ${}^n{C_r}\, = \,{}^n{C_{n - r}}$ we get
$r = x$ and $n - r\, = \,y$
Now, by comparing both the equations we got the value of $x$ and $y$ as $r$ and $n - r$ respectively.
So, now we can find the value of $x + y$as,
Substituting values of $x$ and $y$ in $x + y$ we get,
$x + y\, = \,r\, + \,n - r$
$ \Rightarrow \,x + y\, = \,n$
Thus, we get the value of $x + y$ as $n$
Additional Information: Combination is the selection of required number of things from the total number of things, without considering the order of the things. And when the order is important we use permutation. Both of these permutation and combination have different formulas and they are used as per the condition mentioned. The formula to calculate the combination is given as ${}^n{C_r}$ where $n$ is the total number of things and out of it $r$ things are selected.
And combination formula is given as
$C\left( {n,r} \right)\, = \,\dfrac{{n!}}{{r!\left( {n - r} \right)!}}$ (! Symbol is the factorial symbol )
For ex, $3!\, = \,3 \times 2 \times 1\, = \,6$
Also if ${}^n{C_r} = \,{}^n{C_y}$ then we can say $x = y$ or $x + y = n$
Note: Be careful while comparing the value of $x$ and $y$ with the desired property of combination, that is ${}^n{C_r} = {}^n{C_{n - r}}$. There are various other properties of combination, we have to choose them according to the given condition in question. Also after finding the values to $x$ and $y$ , don’t leave the question there, as we are asked to find their sum.
Formula used: ${}^n{C_r}\, = \,{}^n{C_{n - r}}$ where $n$ is total items and $r$ is selected number of items.
Complete step-by-step answer:
According to question we are given,
${}^n{C_x}\, = \,{}^n{C_y}$ and we have to find the value of $x + y$
As we know the property of Combination which says ${}^n{C_r}\, = \,{}^n{C_{n - r}}$
So, comparing both of the equations that is,
${}^n{C_x}\, = \,{}^n{C_y}\,$ and ${}^n{C_r}\, = \,{}^n{C_{n - r}}$ we get
$r = x$ and $n - r\, = \,y$
Now, by comparing both the equations we got the value of $x$ and $y$ as $r$ and $n - r$ respectively.
So, now we can find the value of $x + y$as,
Substituting values of $x$ and $y$ in $x + y$ we get,
$x + y\, = \,r\, + \,n - r$
$ \Rightarrow \,x + y\, = \,n$
Thus, we get the value of $x + y$ as $n$
Additional Information: Combination is the selection of required number of things from the total number of things, without considering the order of the things. And when the order is important we use permutation. Both of these permutation and combination have different formulas and they are used as per the condition mentioned. The formula to calculate the combination is given as ${}^n{C_r}$ where $n$ is the total number of things and out of it $r$ things are selected.
And combination formula is given as
$C\left( {n,r} \right)\, = \,\dfrac{{n!}}{{r!\left( {n - r} \right)!}}$ (! Symbol is the factorial symbol )
For ex, $3!\, = \,3 \times 2 \times 1\, = \,6$
Also if ${}^n{C_r} = \,{}^n{C_y}$ then we can say $x = y$ or $x + y = n$
Note: Be careful while comparing the value of $x$ and $y$ with the desired property of combination, that is ${}^n{C_r} = {}^n{C_{n - r}}$. There are various other properties of combination, we have to choose them according to the given condition in question. Also after finding the values to $x$ and $y$ , don’t leave the question there, as we are asked to find their sum.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)