Aptitude Discussion

Q. |
A college has $10$ basketball players. A $5$-member team and a captain will be selected out of these $10$ players. How many different selections can be made? |

✔ A. |
$1260$ |

✖ B. |
$210$ |

✖ C. |
${^{10}C_6} × 6!$ |

✖ D. |
${^{10}C_5} × 6$ |

**Solution:**

Option(**A**) is correct

A team of $6$ members has to be selected from the $10$ players. This can be done in ${^{10}C_6}$ or $210$ ways.

Now, the captain can be selected from these $6$ players in $6$ ways.

Therefore, total ways the selection can be made is,

$210×6 = \textbf{1260}$

**Alternatively**, we can select the $5$ member team out of the $10$ in ${^{10}C_5}$ ways $= 252$ ways.

The captain can be selected from amongst the remaining $5$ players in $5$ ways.

Therefore, total ways the selection of $5$ players and a captain can be made

$= 252×5$

$= \textbf{1260}$

**Ashish**

*()
*

captain can be selected in 10 ways

other 5 can be selected in $^9C_5$ ways

So ans $= ^9C_5 * 10 =1260$