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

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Math Expert
Joined: 02 Sep 2009
Posts: 50623
A certain school principal must choose 5 students to attend a field tr  [#permalink]

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08 Apr 2016, 01:52
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:37) correct 47% (01:48) wrong based on 69 sessions

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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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Location: India
Concentration: Strategy, General Management
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Re: A certain school principal must choose 5 students to attend a field tr  [#permalink]

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08 Apr 2016, 20:10
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

Director
Joined: 24 Nov 2015
Posts: 522
Location: United States (LA)
Re: A certain school principal must choose 5 students to attend a field tr  [#permalink]

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14 May 2016, 21:38
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
Manager
Joined: 24 Dec 2016
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Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: A certain school principal must choose 5 students to attend a field tr  [#permalink]

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23 Mar 2017, 22:30
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
Re: A certain school principal must choose 5 students to attend a field tr &nbs [#permalink] 23 Mar 2017, 22:30
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