Question

A village has $10$ players. A team of $6$ players is to be formed. $5$ members are chosen first out of these $10$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is

• A. $1260$
• B. $210$
• C. $\left({{}^{10}C}_6\right)5!$
• D. ${{}^{10}C}_{5}6$

Answer 1

The correct option is A $1260$

A village has $10$ players.

Now a team of $6$ players is to be formed.

Thus $1^{st}$ we select the $5$ players from total $10$ players in ${{}^{10}C}_5$ ways and $6^{th}$ person will select from the remaining $5$ players in $5$ ways.
Total number of ways $={{}^{10}C}_5\times 5=1260$