DIRECTIONS for the question:Solve the following question and mark the best possible option.
A college has 10 basketball players. A 6-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)
10C6×6!
D)
10C5×6!
E)
None of these
A
A team of 6 members has to be selected from the 10 players. This can be done in 10C6 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 10C5 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.
