# Moderate Permutation-Combination Solved QuestionAptitude 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

$= 252×5$

$= \textbf{1260}$

## (1) Comment(s)

Ashish
()

captain can be selected in 10 ways

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

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