Answer
414.9k+ views
Hint: To solve this question, we should know the details about the non-fixed places in the team and the players who are always excluded or included. The number of ways of selecting “r” players out of players is given by${}^n{C_r}$. Using this formula, we can get the answer.
Complete step by step answer:
In the question, It is given that a team of $10$ players out of $22$ players. Here are $6$ particular players always to be included and $4$ particular players are always excluded.
Therefore, we can write the total numbers of players $ = 22$
We have to find that we need to select the team of $10$ players
We have to exclude $4$ particulars players of them
So we have to subtract it as the total number of players
Now we have only $18$ players are now available.
Also, from these $6$ particulars will always be including.
$\therefore$ The required number of ways $ = {}^{12}{C_4}$.
Note:
In these types of problems, we need to know the key concept of permutation and combination. Students can make a mistake by not considering the constraints given in the question.
That leads to a selection of $10$ out of $22$ players which can be written as ${}^{22}{C_{10}}$$ = {}^{22}{C_{22 - 10}} = {}^{22}{C_{12}}$ which leads to a wrong answer.
Generally, students get confused between permutation and combination.
If you have to select, then use a combination, and if you have to arrange use permutation. It is a very nice trick to use. Do not forget to use the correct way otherwise you will get the wrong answer.
Complete step by step answer:
In the question, It is given that a team of $10$ players out of $22$ players. Here are $6$ particular players always to be included and $4$ particular players are always excluded.
Therefore, we can write the total numbers of players $ = 22$
We have to find that we need to select the team of $10$ players
We have to exclude $4$ particulars players of them
So we have to subtract it as the total number of players
Now we have only $18$ players are now available.
Also, from these $6$ particulars will always be including.
$\therefore$ The required number of ways $ = {}^{12}{C_4}$.
Note:
In these types of problems, we need to know the key concept of permutation and combination. Students can make a mistake by not considering the constraints given in the question.
That leads to a selection of $10$ out of $22$ players which can be written as ${}^{22}{C_{10}}$$ = {}^{22}{C_{22 - 10}} = {}^{22}{C_{12}}$ which leads to a wrong answer.
Generally, students get confused between permutation and combination.
If you have to select, then use a combination, and if you have to arrange use permutation. It is a very nice trick to use. Do not forget to use the correct way otherwise you will get the wrong answer.
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)