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From a team of 6 students, in how many ways can we choose a captain an 30 Jul 2021, 20:10
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

77% (00:34) correct 23% (00:34) wrong based on 182 sessions

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From a team of 6 students, in how many ways can we choose a captain and vice-captain assuming one person can not hold more than one position?

A. 10
B. 6
C. 30
D. 2
E. 15
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C
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From a team of 6 students, in how many ways can we choose a captain an 30 Jul 2021, 21:20
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Solution:

There are a number of ways of solving this question. We will apply the filling space method.

So the first space i.e., the captain's position can be filled by \(6\) students.

After that the second space i.e., the vice-captain's position can be filled by \(6-1=5\) students.

So the total number of ways captain and vice-captain can be selected \(= 6\times 5=30\)

Hence the right answer is Option C.
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From a team of 6 students, in how many ways can we choose a captain an 24 Aug 2021, 06:11
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GMATWhizTeam - Thank you for sharing the solution. Can you please explain why order doesn't matter here? Why is \(^6C_2\) incorrect in this case?

GMATWhizTeam
Solution:

There are a number of ways of solving this question. We will apply the filling space method.

So the first space i.e., the captain's position can be filled by \(6\) students.

After that the second space i.e., the vice-captain's position can be filled by \(6-1=5\) students.

So the total number of ways captain and vice-captain can be selected \(= 6\times 5=30\)

Hence the right answer is Option C.
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From a team of 6 students, in how many ways can we choose a captain an 12 Sep 2021, 00:20
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kaladin123
GMATWhizTeam - Thank you for sharing the solution. Can you please explain why order doesn't matter here? Why is \(^6C_2\) incorrect in this case?

GMATWhizTeam
Solution:

There are a number of ways of solving this question. We will apply the filling space method.

So the first space i.e., the captain's position can be filled by \(6\) students.

After that the second space i.e., the vice-captain's position can be filled by \(6-1=5\) students.

So the total number of ways captain and vice-captain can be selected \(= 6\times 5=30\)

Hence the right answer is Option C.
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-----------------------------------------------------------------------------

Hey, 6C2 would be incorrect. We don't want one person to hold two positions simultaneously.

To choose a captain, we can do that in 6C1 ways.
Now we have 5 players, and we have to choose the vice captain which can be done in 5C1 way.

Since the two events are dependent on each other, hence we do: 6C1 * 5C1 = 30 (Ans.)

I hope this was clear.

All the best!
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From a team of 6 students, in how many ways can we choose a captain an 18 Sep 2021, 00:40
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Correct Option : 30 - C

Given: 6 student
To find : 1 Captain and 1 Vice Captian
Condition : (no repetition)

Method 1 - Counting Method
- to select captain - 6 ways
- to select vice captain from remaining 5 student - 5 ways
6x5 = 30 ways

Method 2 - Combination
- to select captain - 6C1
- to select vice captain - 5C1
6C1 x 5C1 = 6x5 = 30 ways
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From a team of 6 students, in how many ways can we choose a captain an 21 Feb 2025, 02:29
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