A certain school principal must choose 5 students to attend

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

A certain school principal must choose 5 students to attend

by VJesus12 » Thu Dec 21, 2017 11:55 am

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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

The OA is the option C.

What are the formulas I should use here? Experts, can you help me?

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Source: Beat The GMAT — Problem Solving | Thu Dec 21, 2017 11:55 am

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by GMATWisdom » Fri Dec 22, 2017 8:57 am

VJesus12 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

The OA is the option C.

What are the formulas I should use here? Experts, can you help me?

this question use only one elementary combination formula nCr = n!/[(n-r)! x r!]
5 students combined groups out of 10 students can be made in 10c5 ways =(10)! / [(10-5)! x 5!]=252
and in every group of 5 one treasurer can be selected in five ways and one note taker out of the remaining four can be taken in 4 ways. So number of ways in every group of five one treasurer and one note taker can be taken in 5x4=20ways.
As there are 252 possible groups of 5 students, the total number desired possible ways would be 252x20= 5040
Hence option C is correct.

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field trip

by GMATGuruNY » Fri Dec 22, 2017 9:18 am

VJesus12 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

Number of options for treasurer = 10. (Any of the 10 students.)
Number of options for note-taker = 9. (Any of the 9 remaining students.)
From the remaining 8 students, the number of ways to choose 3 to complete the group attending the field trip = 8C3 = (8*7*6)/(3*2*1) = 56.
To combine the options above, we multiply:
10*9*56 = 5040.

The correct answer is C.

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Re: A certain school principal must choose 5 students to attend

by Scott@TargetTestPrep » Sun Jul 05, 2020 1:58 pm

VJesus12 wrote: ↑
Thu Dec 21, 2017 11:55 am
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

The OA is the option C.

What are the formulas I should use here? Experts, can you help me?

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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