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?
Choose the correct option:
A) 1260	B) 210	C) 10C6 *6!	D) 10C5 *6	E) None
Solution:   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= 
<gadget id="calculator">  210 *6</gadget>
<output>1_260</output>
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= 
<gadget id="calculator">252 *5</gadget>
<output>1_260</output>
1260   Answer: Option 10C6 *6!
<result>C</result>
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?