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. 10C6 × 6!
D. 10C5 × 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 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 = 1260Alternatively
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
This Question Belongs to Arithmetic Ability >> Permutation And Combination
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 ??