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The following question is accompanied by two statements (I) and (II). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. How many different selections can be made?  I) A college has 12 basketball players. II) A 5 member team and a captain will be selected out of the 12 players.

The following question is accompanied by two statements (I) and (II). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. How many different selections can be made?  I) A college has 12 basketball players. II) A 5 member team and a captain will be selected out of the 12 players. Correct Answer Only II

Considering statement I,

The no. of selections is not known

Considering statement II,

A team of 6 members has to be selected from the 12 players

No. of ways = 12C6 = 924 waysThe captain can be selected from these 6 players in 6 ways

⇒ Total ways the selection can be made = 924 × 6 = 5544 ways

Alternatively, the 5 member team can be selected out of the 12 in = 12C5 = 792 ways

The captain can be selected from amongst the remaining 7 players in 7 ways

⇒ Total ways the selection of 5 players and a captain can be made = 792 × 7 = 5544 ways 

∴ The question can be answered using only statement II

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