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What is the correct answer?

4

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. 210

B. 1260

C. 10C6x6!

D. 10C6x6

Correct Answer :

B. 1260


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.

Related Questions

What is the correct answer?

4

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

A. 756

B. 702

C. 720

D. 726

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4

How many Permutations of the letters of the word PIZZA are there?

A. 60

B. 120

C. 240

D. 480

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4

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

A. 159

B. 212

C. 201

D. 209

What is the correct answer?

4

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. 210

B. 1260

C. 10C6x6!

D. 10C6x6

What is the correct answer?

4

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

A. 8*8!

B. 8*9!

C. 7*9!

D. 9*8!

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4

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A. 24000

B. 21300

C. 25200

D. 210

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4

In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?

A. 3! 4! 8! 4!

B. 4! 4!

C. 8! 4! 4!

D. 3! 8!