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A certain school principal must choose 5 students to attend a field tr

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Bunuel
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A certain school principal must choose 5 students to attend a field tr [#permalink] New post   08 Apr 2016, 02:52
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A certain school principal must choose 5 students to attend a field trip out of a group of 10 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?

A. 1,260
B. 2,520
C. 5,040
D. 6,020
E. 10,080
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   08 Apr 2016, 21:10
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Out of 10 students, 5 students can be chosen in 10C5 ways.

Out of the 5 chosen students, note taker role can be taken in 5 ways
Since the note taker role is already taken by 1 student, the treasure role can be taken in 4 ways

Total number of ways = 10C5 * 5 * 4 = 5040

Answer: C
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   14 May 2016, 22:38
5 students can be selected out of 10 students in 10C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 252 * 5 *4 = 5040
correct answer - C
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   23 Mar 2017, 23:30
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Bunuel wrote:
A certain school principal must choose 5 students to attend a field trip out of a group of 10 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?

A. 1,260
B. 2,520
C. 5,040
D. 6,020
E. 10,080


Choosing 5 out of 10 students : 10C5

Out of the chosen 5, we need to select a treasurer and a note taker, i.e., 2 roles. As the same person cant take both the roles, thus, selecting 2 people of the chosen 5 : 5C2
These 2 people can be arranged in 2! ways, i.e., either of them can be a note taker or a treasurer.

So, total ways : \(10C5*5C2*2!\) = 5040
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   02 Jul 2020, 21:29
Can anybody provide some insight into why the second portion is a permutation (5*4) rather than a combination 5C2?

Thank you.
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   02 Jul 2020, 21:54
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mrauj wrote:
Can anybody provide some insight into why the second portion is a permutation (5*4) rather than a combination 5C2?

Thank you.

Its 5C2 only.
5!/3!*2! = 5*2 = 10
That represents in how many ways 2 students as note maker and other representative can be selected.
But it's not necessary that they have to do their assigned work. They can interchange. So that can happen in 2! Ways
So 10*2=20
Which is written as 5*4 as (5*2)*2.

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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   03 Jul 2020, 07:40
Can anyone tell me since there are 10 students to choose from we have 10 options for 1st 9 for second and 8 for third and so on.. why can't we use 10*9*8*7*6 for number of ways to pick 5 students from a group of 10 instead of 10c5
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   03 Jul 2020, 16:40
The final piece is 5C2*2 because:
AB and AB
BA and BA
can be different job selections.
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   10 Jul 2020, 05:38
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Bunuel wrote:
A certain school principal must choose 5 students to attend a field trip out of a group of 10 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?

A. 1,260
B. 2,520
C. 5,040
D. 6,020
E. 10,080


Solution:

First , there are 10C5 = (10 x 9 x 8 x 7 x 6) / (5 x 4 x 3 x 2) = 9 x 2 x 7 x 2 = 252 ways to choose 5 people from 10.

From each group of 5 chosen, the note-taker can be chosen in 5 ways, and, since the note-taker has already been chosen, there are 4 remaining individuals to be chosen as treasurer. Thus, there are 5P2 = 5 x 4 = 20 ways to choose a note-take and a treasurer. Therefore, there are 252 x 20 = 5040 ways to select 5 individuals out of 10 and also select a note-taker and a treasurer.

Answer: C
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Re: A certain school principal must choose 5 students to attend a field tr [#permalink] New post   14 Feb 2024, 15:49
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