# A college has 10 basketball players. A 5 member's 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

**Answer: Option A **

__Solution(By Examveda Team)__

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 = 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

= 1260

## Join The Discussion

## Comments ( 1 )

Related Questions on Permutation and Combination

A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

D. 8! 4! 4!

A. 7560,60,1680

B. 7890,120,650

C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

C. 7 × 9!

D. 9 × 8!

In the picture above at the bottom it is written that the Answer is C but in that it also have a factorial with 6. can u please explain that ??