Question

In how many ways a team of $11$ players can be formed out of $25$ players, If $6$ out of them are always to be included and $5$ are always to be excluded?

• A. $2020$
• B. $2002$
• C. $2008$
• D. $8002$

Answer 1

The correct option is B

$2002$

Step1: Illustration of the number of players:

Total number of players$=25$

Number of players who will be included always $=6$

The number of players who will be excluded always$=5$

So, the number of players left for choice $25-(6+5)=14$

Step 2: Finding the number of ways a team of 11 players can be formed:

In the team of $11$ players $6$ players are always present so we have to select the remaining $5$ players out of $14.$

So, the required number of ways is $$\begin{gathered} {}^{14}{C}_5=\frac{14\times 13\times 12\times 11\times 10}{5\times 4\times 3\times 2\times 1} \\ =2002 \end{gathered}$$

Thus, option (B) is correct.