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**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.

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