# a college has 10 basketball players. a 4-member team and a captain will be selected out of these 10 players. how many different selections can be made?

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## A college has 10 basketball players. A 5

Permutations and Combinations Questions & Answers : A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made

68 Q:

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

A) 1260 B) 1400 C) 1250 D) 1600 Answer: A) 1260 Explanation:

A team of 6 members has to be selected from the 10 players. This can be done in

10 C 6 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

Subject: Permutations and Combinations - Quantitative Aptitude - Arithmetic Ability

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## A college has 10 basketball players A 5 member's team and

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

Examveda

## 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 = 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

### Click here to read 1000+ Related Questions on Permutation and Combination(Arithmetic Ability)

## Join The Discussion

Join The Discussion Comments ( 1 )

Dhruv Sareen : 5 years ago

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 ??

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## A college has 10 tennis players. A 4 member team has to be selected and a non playing captain will be selected out of the remaining players. How many different selections can be made?

A college has 10 tennis players. A 4 member team has to be selected and a non playing captain will be selected out of the remaining players. How many different selections can be made?

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A college has 10 tennis players. A 4 member team has to be selected and a non playing captain will be selected out of the remaining players. How many different selections can be made?

Question

A college has 10 tennis players. A 4-member team has to be selected and a non-playing captain will be selected out of the remaining players. How many different selections can be made?

A 1260 B 210 C 10C6×6! D 10C4× 6 Open in App Solution

The correct option is **A**

10C4× 6

A 4-member team can be selected in

10 C 4

ways. Now as the captain is non-playing he needs to be selected from the remaining 6 players.

Therefore final answer is

10 C 4 × 6 . Option (d) Suggest Corrections 0

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Guys, does anyone know the answer?